Why are baseball pitches that miss the strike zone called "balls"?

The correct definition for this type of "ball", a very shortened call, includes the action taken by the batter, and might still be ambiguous, from a pure linguistic perspective:

c. A throw, toss, or delivery of the ball in a game, esp. (Cricket, Baseball) with the course, speed, etc., of this considered as a measure of its quality or effectiveness. Cf. no-ball n., screwball n. 1, foul ball at foul adj. 14a, wide adj. 11b.
The meaning of the word in quot. 1483 is unclear; the Latin gloss may instead mean something like ‘ball-player, who throws a ball’.
1483 Catholicon Anglicum (BL Add. 89074) (1881) 19/1 Balle, pila, alipatus qui iaculatur pilam.
1773 Gentleman's Mag. Nov. 568 The modern way Of blocking every ball at play.
1824 M. R. Mitford Our Village I. 154 That brilliant hitter..gained eight from two successive balls.
1836 C. Dickens Pickwick Papers (1837) vii. 69 He blocked the doubtful balls, missed the bad ones, took the good ones.
1850 ‘Bat’ Cricketer's Man. (rev. ed.) 54 The names of the bowlers who bowl ‘wide balls’ or ‘no balls’..to be placed on the score.
1935 Times 29 Jan. 5/4 Leyland..missed a straight ball from Constantine, and was out leg-before-wicket.
2007 Daily Tel. (Nexis) 24 Jan. 20 Joyce got his innings going with a sweet cover-drive at a wide ball from Oram.

d. Baseball. A pitch delivered outside the strike zone which the batter does not attempt to hit. Cf. strike n.1 12b, base on balls n. at base n.1 Phrases 3.
1863 Brooklyn Daily Eagle 10 Dec. 2/5 Should a pitcher repeatedly fail to deliver fair balls to the striker, for the apparent purpose of delaying the game, or for any other cause, the Umpire, after warning him, shall call one ball, and if the pitcher persists in such action, two and three balls; and when three balls have been called the striker shall be entitled to his first base.
1912 C. Mathewson Pitching in Pinch 12 It put me in the hole with the count two balls and one strike.
1967 C. Potok Chosen i. 35 He ignored it completely, and the umpire called it a ball.
1986 R. J. Conley Back to Malachi 145 Butcher..let fly another at me. Richard called that one a strike. The next one was another ball, and the next one.
2001 Sporting News 10 Sept. 46/1 There are three balls and two strikes.

— Oxford English Dictionary, This entry has been updated (OED Third Edition, June 2008; latest version published online March 2021).

That means a certain similarity to cricket is obvious from its known heritage, but the differences for calling such a throw any type of 'ball' starts to divert pretty quickly. For example in cricket the 'wide ball' does not depend on the striker not trying to hit 'the ball', the focus is on the action of the bowler, unless the striker does move and comes into a position to reach the ball anyway:

22.1 Judging a Wide

22.1.1 If the bowler bowls a ball, not being a No ball, the umpire shall adjudge it a Wide if, according to the definition in 22.1.2, the ball passes wide of where the striker is standing and which also would have passed wide of the striker standing in a normal guard position.

22.1.2 The ball will be considered as passing wide of the striker unless it is sufficiently within reach for him/her to be able to hit it with the bat by means of a normal cricket stroke.

22.2 Call and signal of Wide ball

If the umpire adjudges a delivery to be a Wide he/she shall call and signal Wide ball as soon as the ball passes the striker’s wicket. It shall, however, be considered to have been a Wide from the instant that the bowler entered his/her delivery stride, even though it cannot be called Wide until it passes the striker’s wicket.

22.4 Delivery not a Wide

22.4.1 The umpire shall not adjudge a delivery as being a Wide, if the striker, by moving, either causes the ball to pass wide of him/her, as defined in 22.1.2 or brings the ball sufficiently within reach to be able to hit it by means of a normal cricket stroke.

https://www.lords.org/mcc/the-laws-of-cricket/wide-ball

For baseball we see the follwoing specifics:

ball

1. A pitch that is not swung at by the batter and that is judged outside the strike zone by the umpire.
2. The baseball itself. 1st Use. 1845. (Knickerbocker Rules).
3. The game of baseball, as in, "he plays good ball." In some childhood circles this term actually overwhelms the proper one. In his autobiography ( The Education of an American, 1938), Mark Sullivan wrote: "We did not know our game as baseball but merely as 'ball,' and in other respects we failed to conform to the orthodox formula."
4. A type of pitch; e.g., fast-ball, screwball, spitball, and curveball.

— Paul Dickson: "The new Dickson Baseball Dictionary", Harcourt Brace & Co., 1999, p29.

That also highlights the differences for how the actions of the batter influence the outcome. However, what the above leaves out is that the strike zone matters in calling what a 'ball':

1907

• A fairly delivered ball is a ball pitched or thrown to the bat by the pitcher while standing in his position and facing the batsman that passes over any portion of the home base, before touching the ground, not lower than the batsman's knee, nor higher than his shoulder. For every such fairly delivered ball, the umpire shall call one strike.

• An unfairly delivered ball is a ball delivered to the bat by the pitcher while standing in his position and facing the batsman that does not pass over any portion of the home base between the batsman's shoulder and knees, or that touches the ground before passing home base, unless struck at by the batsman. For every unfairly delivered ball the umpire shall call one ball.

• The Strike Zone : A History Of Official Strike Zone Rules

So, we see a difference that the batter's pitch is defining the type of ball, and secondary that 'missing the strike zone' is only then a 'ball' when the batter keeps his calm. No action from the batter and foul ball from the pitcher makes the call.

To approach the etymology of the shortened call of 'ball' we need to look at at a newer version of a baseball dictionary:

ball

1. A pitch that is not swung at by the batter and that is judged to be outside the strike zone by the umpire.
   First use, 1863: "Should a pitcher repeatedly fail to deliver to the striker fair balls, for apparent purpose of delaying the game, or for any other cause, the umpire, after warning him, shall call one ball, and if the pitcher persists in such actions, two and three balls; when these balls have been called, the striker shall be entitled to the first base" (Constitution and By-Laws of the NationalAssociation of Base Ball Players, with Rules and Regulations of the Game Base Ball, 1864, Sec 6; John Thorn, who notes that this pamphlet covered the meetings of Dec 9, 1863).

Etymology: Probably shortened version of the original "ball to the bat" […]

— Paul Dickson: "The Dickson Baseball Dictionary (Third Edition)", W. W. Norton & Company, 2011, p47. (gBooks)

Making it again clear that this was/is primarily a call directed at the pitcher, who is the person missing the required target zone.

called ball

1. A pitched ball delivered outside the strike zone and which is not swung at. It is deemed to be a ball by the umpire. The number of called balls required for a walk has varied from nine (1879) to four (1889). […] Syn.: wide, wide one. First use 1886. "Next the Chicagos came to bat, [Abner] Dalrymple reaching first on balls" (Chicago Tribune, May 4, Peter Morris).
2. hist. "The penalty inflicted on the pitcher for unfair delivery. Three balls give a base" (Henry Chadwick, The Game of Base Ball, 1868, p39). In the early days of baseball, the batter requested where the ball should be pitched. If the pitcher did not comply, he was warned that he was throwing unfairly, and a "ball" was called. The batter could not legally hit a called ball, nor could he be put out, First use 1867. "King to bat and off to first on called balls" (Daily National Intelligencer [Washington DC], July 29)).
3. The penalty inflicted when, with the bases unoccupied, the pitcher does not deliver the ball to the batter within the specified time (20 seconds prior to 2007, 12 seconds since 2007) after the pitcher receives the ball and the batter is in the batter's box. The intent of the penalty is to avoid unnecessary delays.

— Dickinson, 3rd ed, p157.

For the etymology of "strike" on StackExchange: https://english.stackexchange.com/questions/43839/how-did-strike-get-its-baseball-meaning

In cricket scoring, a distinction is made between:

1. No-ball: "[A ball] unfairly bowled." - OED (1928)

A “No Ball” can be declared for many reasons: If the bowler bowls the ball from the wrong place, the ball is declared dangerous (often happens when bowled at the batsmen’s body on the full), bounces more than twice or rolls before reaching the batsman or if fielders are standing in illegal positions. - Cricket Rules

2. Wide ball: "[A ball] not properly within the batsman's reach" - OED (1928).

A “Wide Ball” will be declared if the umpire thinks the batsman did not have a reasonable opportunity to score off the delivery. However if the delivery is bowled over the batsmen’s head it will not be declared a wide but a no ball. - Cricket Rules

Together, in sense 4 c. (on pp 638 of Vol. II):

A throw, toss, or "delivery' of the ball in certain games, esp in Cricket, the particulars of its course and effect being included in the notion.

In baseball, where no distinction is made between the two, terming them both simply "balls" seems the most reasonable simplification of terminology.

Prior to 1901 the Rules of baseball changed frequently, often annually, including numerous adjustments to the terms under which a pitch was fairly delivered to the batsman and in turn swung at by the batsman:

In 1880, a batter was out if the catcher caught the third strike; otherwise, the batter got four strikes. Before 1883, pitchers were required to deliver pitches with their hand below their hips; in that year, the rule was changed to allow shoulder-high deliveries. Until 1887, batters could call for either a high or low pitch, and the strike zone was either above or below the waist. In 1885, the rules changed, until 1893, to allow bats to be flat on one side; beginning in 1893, they had to be round. In 1887, the rules changed so that batters could no longer call for a pitch; and the strike zone was defined as from the shoulders to the knees. During this period, the pitcher's mound was much closer to home plate, foul balls were not counted as strikes, batters got four strikes, and the number of "called balls" resulting in a walk—which initially included strikes and foul balls- went from 9 to 8 to 7 to 6 to 5 and, in 1889, to 4. In that same year, the number of strikes went from 4 to 3.

As the above notes, there was an extensive and wide varying experimentation on the terms of delivering a ball to the batter and fairly swinging at it, over several decades. That a condensation of terminology occurred as noted above seems only natural. That baseball evolved from a family of similar games including cricket, rounders, and the like, and replaced cricket in popularity about the time of the Civil War, is not in dispute. The rather sudden replacement of cricket by baseball as a national pastime, in the 1860's and 1870's, would adequately account for the carry over of terminology from the former by the latter as Knickerbocker Rules popularized.