Could skirmishers pass through friendly formations in ancient/medieval warfare?

This is not going to rise the level that I consider the minimum for a good answer, but it is getting longer than a simple comment. I also don't have time to deliver a complete answer, so these are some notes

The equipment of the velites, who were light infantry skirmishers that screened and supported the legion, would have been much cheaper than the equipment of the rest of the infantry (who were all armored, heavy infantry) ACOUP

In this model the skirmishers screen and support - there is no need for them to move through the heavier units. I think that elsewhere ACOUP asserts (in line with other authors I've read) that the outcome of a battle depends heavily on where the two armies choose to do battle (and that this is one of the very few decisions that pre-modern generals get to make). Skirmishers are essential in helping to force that selection, taunting the adversary onto ground that is advantageous, or harassing them away from terrain that is comparatively disadvantageous.

As noted above, there is a second model for skirmisher:

"Acting as light infantry with their light arms and minimal armour, they could run ahead of the main battle line; release a volley of arrows, sling stones, or javelins; and retreat behind their main battle line before the clash of the opposing main forces.

I'm not sure that this required a huge amount of organization. I had a friend who played with the Society for Creative Anachronism, who said that one of the most impactful memories was of a lightly armored scout walking backwards just out of reach of a lance of knights on foot, taking notes on numbers and names, so that he could report back to his army. He was just outside weapons reach, but there was no way for the lance to maneuver to catch him - he didn't have to be fast, he just had to be slightly faster than a bunch of knights in armor in formation.

I can well imagine (but can't find any evidence at this point) that this model of skirmish would work similarly. Skirmishers have enough mobility that the adversary can either break formation or else just endure the harassment.

A "formation" automatically included gaps See ACOUP. I'm no expert in infantry tactics, but the larger the formation is the less agile. Building in gaps improves the nimbleness and ability to shift/reform. (ACOUP also alludes to this in the set of articles that govern the supply of larger armies.)

Romans practiced an evolution that opened the formation to allow forward fighters to pass through to the rear. Rotating skirmishers through lines prior to the contact of battle would be, I imagine, much simpler, but it is my impression_ that few pre-modern armies reached that level of professionalism, so it is probably the exception rather than the rule.

I'm trying to think of other sources I'd consult ACOUP has a couple of other articles in the Generalship series that describe the first model - but I'm coming up blank on other sources for the second. I invite community participation in the comments.

My answer is to simply bring up some human factors in this kind of maneuver, from someone who has had a bit of military experience.

Yes, you could have skirmishers pass through friendly formations as they pull back. But in most cases, it will likely not be pretty nor appreciated.

Small unit commanders - think about a platoon sergeant or a company lieutenant - tend to be possessive over their men, the area they occupy, and so on. "This is my patch of ground, all others stay off" is a very typical mindset. The presence of another unit running through is often a problem for the commander, since now some chaos is happening in their formation. His ability to control his own men and the situation in general is degraded while that other unit is passing through.

Let's take an example of a typical Roman phalanx in pycne formation (fighting formation, not too open, not tightly closed like riot police). If I'm the commander of that unit, I'm already keyed up because I've been marching my men around and trying to maintain their proper position and spacing. The spacing is very important for combat, since each soldier needs working space - not too much, not too little. If I see friendly skirmishers falling back on my formation, the last thing I want is for them to pass through my formation because contact is likely to happen in about thirty seconds and I need control and my men need their spaces to not be occupied by wayward friendlies. I'm going to frantically wave my arms for them to go around my formation, not through it.

If they do come through my formation, I'm going to be shouting and shoving them to get through my formation as fast as possible, and for heaven's sake do not stop in the middle to watch the action. I may very well smack any who pause in my formation with the flat of my gladius.

Now you could say that my formation should have been in eis bathos formation - very open spaces - for the skirmishers to come through, then close up to pycne once they are through, but it's unlikely - if there's less than thirty seconds until the enemy arrives, then it's a dodgy time to be changing formation. I personally would rather be in fighting formation before that time because it suits my formation the best - recall that I command a unit of heavy infantry and I'm going to look out for its interests, and the skirmishers are not so much my concern (they have their own commander, after all).

So if most unit commanders wanted skirmishers to go around and not through, then the obvious correlation is that there are gaps between formations, and this happens quite easily. When I said that small-unit commanders are possessive over their men and space, they often tend to be more concerned with their core space and not so concerned about maintaining close contact with their neighboring formations. It requires a higher level of training, and a lot of monitoring by headquarters, to make sure units don't open gaps with their neighbors. It takes skill in the first place to arrange units such that they can be in their natural fighting stance and have minimal gaps between them.

Formations keeping contact with their neighbors has been an age-old challenge for armies and there are many examples of an army being defeated by having those gaps found out exploited, even at the divisional or army level. A more recent and massive example was the 1973 October War, when the Israelis found the gap between the Egyptian Second and Third Armies and took full advantage of it.