Why does Satan collect souls that are subservient to him according to mainstream Christian scriptures?

He doesn't. He just happens to be where people who reject the Light go. A drain doesn't pull water to it. He was just there first.

Why does Satan collect souls according to Christian scriptures?

The Devil has been described as granting magical powers to sorcerers and witches, usually in exchange for worship or souls. In Acts of the Apostles 16:16 Paul the Apostle meets 'a slave girl who had an evil spirit that enabled her to predict the future'. He performs an exorcism using the name of Jesus Christ (Acts 16:16-19)- Devil in Christianity

The Adversary called the Satan desires nothing else but the ruin of souls, yours, mine as well as the soul of every Tom, Dick and Harry in the world. He wants everyone to be in hell with him and just as miserable and hate filled as he is.

We are warned in Sacred Scripture to be on guard against the operation and works of the Devil.

Be sober, be vigilant; because your adversary the devil, as a roaring lion, walketh about, seeking whom he may devour. (1 Peter 5:8)

Satan is miserable at all times for he knows not what love is and seeks the ruin of us all. Just look how he treated Job, destroying his family and all he possessed and eventually covering him with a terrible skin illness. Yet in all things Job did not Sin. Job remain vigilant and faithful to his Creator.

But the dragon was not strong enough, and no longer was any place found in heaven for him and his angels. And the great dragon was hurled down—the ancient serpent called the devil and Satan, the deceiver of the whole world. He was hurled to the earth, and his angels with him (Rev 12:8-9).

The LORD said to Satan, “Where have you come from?” Satan answered the LORD, “From roaming throughout the earth, going back and forth on it” (Job 1:7).

Let us remembers St. Paul's words about who we have to deal within this life:

For we wrestle not against flesh and blood, but against principalities, against powers, against the rulers of the darkness of this world, against spiritual wickedness in high places. (Ephesians 6:12)

Be always on one's guard, for we know not when he will strike.

Jesus says that the eternal fire of hell was “prepared for the devil and his angels” (Matt. 25:41). People were made for God. Hell was made for the Devil. Yet people who die in their sin, without Jesus Christ as Lord and Savior, will spend eternity in hell with the one being who is most unlike God. It is a tragic irony that many who do not believe in the Devil in this life will wind up spending eternity being tormented with him in hell. - 4 Truths About Hell

Do not let Satan take a foothold in your soul, lest the Devil would enter your heart as what happened to Judas Iscariot. The Adversary is always searching for soul to do his deeds and lead others astray.

Be Vigilant!

"Men who are damned are not occupied in drawing others to damnation, as the demons are." (Summa Theologica, Suppl., Q. 98, a. 6, ad. 2)

According to my reading of scripture, particularly Revelation 20:7-10 (https://www.biblegateway.com/passage/?search=Revelation+20%3A7-10&version=NIV), after the final judgment, Satan, fallen angels and all rebellious humans will be imprisoned. Nothing is said about there being any hierarchy in Hell. As far as I know, Satan will be a regular prisoner like all the others, with no authority over anyone.

Until then, however, Satan exercises influence over some people. Some people are demonically or Satanically possessed, such as Judas. (https://www.biblegateway.com/passage/?search=Luke+22:3&version=NIV)

Satan's main sin is generally considered to be pride; he wants to be in charge, to supplant God. Thus all his efforts are aimed at opposing God's authority and asserting his own. (https://www.biblegateway.com/passage/?search=Isaiah+14%3A12-15&version=NIV)

Update:

One more verse that sheds light on this is in Luke:

“I tell you, my friends, do not be afraid of those who kill the body and after that can do no more. But I will show you whom you should fear: Fear him who, after your body has been killed, has authority to throw you into hell. Yes, I tell you, fear him. (Luke 12:4-5, NIV)

This directly answers the question of who is in charge of souls, Satan or God. Satan has power over human souls and bodies (within the limits set by God, such as the hedge around Job) in this life. In the life to come, all control over souls is in God’s hand.

I have not found a statement referencing Satan collecting souls in any of the mainstream Christian documents.

I think this page gives a good overview of the doctrine of Satan according to the scriptures: Satanology.

A better question might be “Is there any biblical basis for thinking that Satan collects souls that are subservient to him?” That’s because there is no such teaching according to mainstream Christianity.

The idea that Satan “collects souls” is neither biblical nor Christian. The Bible tells us that every living soul belongs to God” (Ezekiel 18:4) and that only God has the power to kill the soul (Matthew 10:28). Jesus also said that there is an eternal fire prepared for the devil and his angels (Matthew 25:41) and that Jesus has the keys of death and hades (Matthew 16:18). Hebrews 9:27 informs us that “man is destined to die once and face judgment”. This is God’s judgment, not Satan’s. Wherever the souls of persons who have physically died end up is entirely according to God’s will, not Satan’s.

Nothing in all creation is hidden from God’s sight. Everything is uncovered and laid bare before the eyes of Him to whom we must give account” (Hebrews 4:13).

There are some denominations, however, that appear to subscribe to the power of Satan and his demons with regard to having control over the souls of the dead:

‘Aerial toll houses’ refer to a teaching held by some Eastern Orthodox saints and Eastern Orthodox Christians about the immediate state of the soul after death. It holds that "following a person's death the soul leaves the body, and is escorted to God by angels. During this journey the soul passes through an aerial realm, which is inhabited by wicked spirits (Ephesians 6:12). The soul encounters these demons at various points referred to as toll-houses where the demons then attempt to accuse it of sin and, if possible, drag the soul into hell."[1]

In some forms, the teaching is taught in hagiographical and other spiritual texts from quite early in the history of the church, but it has never been formally promulgated by any ecumenical council.[1] A number of the Orthodox saints, modern elders and theologians have openly endorsed it, but some theologians and bishops, starting from the last century, have condemned it as heretical and gnostic in origin.[2] The content is somewhat similar to that propounded by John Climacus in The Ladder of Divine Ascent. Some say that given the amount of fear that comes along with the teaching, the love of Christ becomes misunderstood and is forgotten, but others suggest that fear is perfectly natural and salvific for Orthodox Christians. Source: https://en.wikipedia.org/wiki/Aerial_toll_house

Another source of “misinformation” comes from ‘The Divine Comedy’, written by Dante Alighieri between 1308 and 1321. It is written in the first person as Dante describes his imaginative journey through the three realms of the dead: Inferno (hell); Purgatorio (Purgatory); and Paradiso (heaven). Dante describes hell as comprised of nine concentric circles, representing an increase of wickedness, where sinners are punished in a fashion befitting their crimes. At the bottom of hell, Satan waits to gorge on the miserable creatures who reach him.

Dante’s literary vision of hell is depicted by Botticelli in his painting Map of Hell as a subterranean funnel of suffering—a wretched underground landscape of fire, brimstone, sewage, and monsters, with Satan himself waiting at its core. It’s all very disturbing, and effective as a work of art, but it is based on the imaginations of men, not the Word of God.

In Dante's Inferno, Satan is portrayed as a giant demon, frozen mid-breast in ice at the center of Hell. As opposed to the popular conception of the era, which viewed Satan as an all-dominating beast of Hell, Dante gives the portrayal of Satan as simply another victim of Hell's tortures. He places Satan trapped within the ice, stripped of voice and power and thus sets forth a new conception of who and what Satan is. Source: https://en.wikipedia.org/wiki/Dante%27s_Satan

These views do not represent mainstream Christian beliefs about what happens to the soul at death. Jesus said:

Depart from me, you who are cursed, into the eternal fire prepared for the devil and his angels (Matthew 25:41).

God and Jesus are in control. End of.