Is this depiction of command hierarchy, with the chain of command standing next to each other, historically accurate?

Duty to Refuse: An additional aspect not yet covered in any answer is that (in an American context), every officer has a duty to refuse unlawful orders (as do the enlisted), and NO duty to "follow the orders of the president and the offiers appointed over me". That quote is only present in the Oath of Enlistment, not in the officer's oath. By following the chain of command even in close proximity, every officer has been given an opportunity to exercise his duties.
Right to Remove: Finally, if the senior officer present wishes to override a subordinate's balkiness, he must remove that officer. This he may do at will, but until he does, the men under the subordinate officer's command remain more tightly bound to the subordinate's orders.

Please consider this answer a supplemental offering to any other answer.

There is also the matter of confusion during times of combat.

What with explosions, fire, casualties, etc... it can be an extremely chaotic and disorienting moment.

Soldiers are trained by repetition to follow the orders of their immediate superior, so that they don't inadvertently take the wrong action when everything else is chaos and confusion.

In the midst of a major attack, with shells exploding, bullets flying, and people screaming, an officer says to a sergeant - go cover that southern approach. You don't want three squads of soldiers to go running to the southern approach, just because they heard that, leaving the other approaches unguarded. They wait until their sergeant gives the actual order.

Same is true if there are two or three sergeants shouting orders over all the noise. Unless a superior officer singles out a subordinate not normally in their chain of command, soldiers do what their immediate supervisor says, to avoid any misunderstanding.

One has to put this in the context of the chaos of actual combat to appreciate the necessity for an absolutely clear chain of command. In that situation, people are reacting on instinct and training, because their rational mind is too overloaded to reach any sort of conclusion.

Imagine the opening scenes of Saving Private Ryan...

Hardly an "academic" answer, I'm a middle-aged (alright, elderly) woman with no military experience, though from a family of soldiers - but it seems blindingly obvious to me. Officers have to communicate with each other, and with those under their command, clearly and unambiguously. A non-military analogy (with no inferences re hierarchy to be drawn!) -

Kid: Mum, there's the ice-cream van - can I get one?

Mum: No, I'm just about to dish up dinner.

Kid, going to another room: Dad, can I get an ice-cream?

Dad: Sure, son, here's some money!

Tears before bedtime!

As stated by this British Army Doctrine Publication, an clear chain of command

strengthens integration between formations and units and enhances unity of effort. Subordinates must be in no doubt as to the command state within which they are operating, to whom they are responsible and for what.

The chain of command in the British army at the turn of the 20th century was far from ideal (on which more below), but first a few other key points on the benefits of an effective chain of command.

US Army Regulation 600–20, Army Command Policy (Headquarters, Dept. of the Army, Washington DC, 7 June 2006), Chapter 2.1 gives the 'official' view on Chain of Command:

Section B

Commanders are responsible for everything their command does or fails to do. However, commanders subdivide responsibility and authority and assign portions of both to various subordinate commanders and staff members. In this way, a proper degree of responsibility becomes inherent in each command echelon.

Section C

Proper use of the chain of command is vital to the overall effectiveness of the Army....Effective communication between senior and subordinate Soldiers within the chain of command is crucial to the proper functioning of all units. Therefore, Soldiers will use the chain of command when communicating issues and problems to their leaders and commanders.

The article The Successful Lieutenant by Captain Christopher J. Courtney in the Military Intelligence Bulletin gives the following advice to Lieutenants, pointing out the need to let those below you in the chain learn how to command. If senior officers are the only ones giving orders, others are being denied the chance to develop as leaders.

Lead Through Your NCOs. You must do everything you can to empower, support, and resource your platoon sergeant and squad leaders. Let them execute your orders without excessive guidance and interference....You should seldom, if ever, give an order directly to an individual soldier. As a rule of thumb, you give orders to the platoon sergeant and squad leaders who execute the mission. In addition, do not let your soldiers jump their chains of command to see you, except in rare cases, such as equal opportunity or sexual harassment. Allowing soldiers to jump the chain of command cheats your NCOs out of the chance to lead and weakens the overall leadership of the platoon.

The chain of command in the British army up to and including World War I was undermined by social hierarchy, mistrust and a lack of meritocracy, despite the abolition of the Purchase of commissions in the British Army in 1871. On the British military,

For example, during World War I the army chain of command on the western front was accused of being rigid and unresponsive, in part as a result of an overweening deference to authority and hierarchy among army personnel.

and

The command structure was based on obedience to superiors and suspicion of subordinates. . . . Inhibitions existed at every level. Orders were issued at the top and fed down the line; there was little traffic in the other direction

Citing Niall Ferguson, 'The Pity of War: Explaining World War I'

In an effective chain of command, superiors must demonstrate their trust in subordinates. Breaking that chain by going directly to a subordinate of a subordinate - except in unavoidable circumstances - would be showing a lack of respect and / or confidence.

This is absolutely no different from a modern office environment. The only person I take orders from is my supervisor. Anyone above/outside him will be politely told, "I need to check that with Mr. M." or "Please coordinate that through Mr. M". (In many cases it is illegal for me to take direction from anyone other than Mr. M.; it can result in civil/criminal penalties).

In a high stress environment, you want someone you trust to take care of you. Guns going off, bullets and shells killing people to the left and right of you. You want to listen for and hear one voice. You do not want any confusion. From the point of view of the tip of the spear, there is no chain of command; there is only the guy who you trust to pull your fat out of the fire. Senior officers can jabber all they want and can issue commands to a dozen different units; that's all noise until your guy says the words.

From the top down, you don't want soldiers and sailors listening to and decoding all the orders (not cause you don't trust them, but because you want them focused on the enemy.) If you're going to issue commands to a dozen units, or if you're going to issue commands to only one, you want those commands to be carried out. The guy who is closest to those troops is the best/most capable of ensuring that. Of knowing what words will motivate the appropriate urgency.

When I was military we ran annual exercises, many of which ended in disaster - usually because some mid level officer used a word in a context that made sense to a senior officer, but didn't match the tactical training. The best example I can give is the year that someone issued a report that said that orange forces conducted a strike on position X. Half an hour later the entire exercise was in shambles, because to the operators "strike" was used only for nuclear weapons. Conventional forces "attack" a position, but strategic forces "strike". (not strictly a chain of command example, but I hope it illustrates the importance of knowing how the recipient of the orders uses the words).

The reason you've got those mid level officers is to understand the strategic objective and to deploy the right tactical resources to get it done.

Why are they rigorous about it? Because the military is centuries of tradition, and one of the primary traditions is to avoid progress unless necessary. The machine works because all the participants known and understand their roles.

I acknowledge my own hypocrisy; this is an answer with no resources/citations. I hope it adds something to the other answers

• Emphatically agree with Mr. Geerkens that training, of all levels of responsibility, is reinforced by this constant repetition. In a stress environment people will fall back on their training. (which is also why the military is centuries of tradition with as little innovation as possible).

• Clarity for the soldiers.
  Imagine you are a a rifleman standing or crouching somewhere during the battle. The colonel says in your hearing "hold this position." The captain says "first platoon, face left." The lieutenant says "third section, infantry on the slope, five rounds rapid, then fall back."
  What are you to do? Are you supposed to judge how falling back helps to hold the position? Much clearer if you can simply obey the chain of command, unless the superior officer explicitly relieves the junior officer.
• Clarity for the officers.
  The commanding officer of an unit is responsible for anything the unit does or fails to do. How can he be held responsible if he gets bypassed by his superiors?