So I'm going to go ahead and run against the grain here and say that I do not subscribe to the "pulse" school of melee combat at all. The only time period and region that I know of where it is even a viable theory is in the Greek Cities roughly between about 500BC and 250BC. Its almost absurd to make assumptions about the entirety of warfare in antiquity based on one society in one small peninsula in the late Bronze age.

I think its somewhat reasonable to imagine the "pulse" method being used during the hoplite Wars of Greece during the Golden age as this was a highly organized society with highly ritualized warfare. The men fighting the battles were typically wealthy, landowning, citizens who were invested in maintaining the warrior traditions of that culture and they would have known the cues that signaled when both sides would call time-out. This isn't to say that I totally buy the whole idea just that it seems possible in this particular context.

Now lets turn to why I think the whole idea is completely ridiculous: maintaining the initiative is the key to winning battles, you want to dictate the terms of the engagement to the enemy. Taking a break in the middle of fighting gives the enemy an opportunity to recover the initiative, what commander is going to allow that to happen? Yes men get tired during battle, it is rigorous and exhausting but if your men are tired so are the enemy's! That is good, a tired enemy is better than a fresh one.

In addition it is incredibly difficult to get large groups of people to do anything at once. In large armies not fighting in the ritualized style of the Greeks how would one know to disengage? What happens if one part of the line disengages and the other doesn't? And lastly what advantage do you gain from disengaging?

I hope my response doesn't seem anecdotal it is grounded in solid theory and strategy.

The typical understanding of the othismos doesn't make sense as an effective way to fight simply due to physiology. I think a great example of this is American Football.

American Football players are armored in a very similar manner to hoplites, sure it's a little lighter and more comfortable but it's made of the same basic components. American football players do a great deal of pushing. They don't carry shields or spears but at some point many of the same strategical points and simple human behaviors come into play.

First you can't willingly run into something without bracing for it. Try running head first into a wall without throwing up your arms or having your feet enter a natural bracing stance moments before you hit. Bet you can't do it. I've never met anybody who could. Now find somebody to charge you and knock you down. Bet they lower their shoulder and I bet you do to before they hit you. Standing up is not a natural way to impact. So before impacting I assume the individuals in an army would enter some form of crouch behind the aspis. The only other option is a headlong dash into an opponent. This at best results in you being rebuffed with some small pain and at worst ends in you overwhelming him and then lying on top of him slightly dazed for about 2 seconds, alone, with the entire opposing army forming up around you.

Second If an individual is in an optimized stance for pushing there is little additional strength added by pushing him in a way that would move him forward. Optimal pushing is done with your body at about a 45 degree angle to the ground with feet shoulder width apart knees bent strong leg half a stride ahead of weak leg. If you lean more than 45 degrees you are prone to tipping over and falling on the ground. If you lean less your opponent is likely to get underneath you and push you over. In this position I can push with about 900 lbs force if I have good footing. Getting good footing is the key. The best American Football linemen learn how to drive their feet constantly running in place resetting their footing and generating extra power through leg momentum. This takes quite a bit of practice to do properly. It also leaves you prone to overwhelming your opponent again possibly leaving you alone and dazed surrounded by the enemy. So fixed footing is more likely. This actually can be assisted slightly by placing your foot behind their back foot and setting your shield on their back but not pushing unless the front man is pushed back significantly above 45 degrees. Any movement must come from the front/pushing mans own controlled movement of his feet. This is great actually because in a position like this you are in a relatively braced position and also free to stab about with your spear.

Now, if anybody mentions rugby scrums I'm going to lose it. Rugby scrums, like goal line offense/defense in American Football, ends as often as not in pretty much everybody falling on the ground in a heap. If this were to happen the three scenarios that could happen are; people fight on the ground rolling around and wrestling, everybody who fell down gets stabbed by those still standing up, or everybody falls down gets back up falls down again and repeats like a terrible slapstick comedy. None of these scenarios match the descriptions given of ancient battles.

Third in a pushing battle somebody eventually loses and the one who loses generally loses catastrophically. One person either falls down or rises too high. Fall down you get stabbed rise too high, well, once I get underneath you I have 900 lbs of force working against your maximum force of only your body weight. If I throw you right I have a local force of my momentum at about 1.5X my body weight plus your momentum at 1.5X your body weight plus my pushing force so as much as about 1300lbs of force. That's enough force for me to knock over several rows of men who aren't braced properly for pushing, remember without bracing for a push the maximum force is body weight.

Fourth pushing from the side is easy. If I defeat the guy directly in front of me even for just a few seconds and then can push from the side at the men on either side of me I have a decent chance of starting a chain reaction of failures along my opponents front. Many if not most of these failures will result in my opponent stumbling backward in some manner. This creates momentary respite and also space. Unfortunately the space is probably clogged with a few bodies (fallen, injured or dead both friend and enemy)

Fifth pushing is really tiring. If I can create that space I probably wont have the energy to pursue. after a couple of rounds I'll probably have enough energy to pick up my comrades and reform my line. Then with about 30 seconds to 1 min of recovery I can do it all again. That 30 seconds to 1 min of recovery are a lifesaver. Without them in American Football you just get two 300lb men leaning against each other to avoid falling down. I imagine it would be similar for ancient combatants.

The basic premise of my long and rambling post is that pushing has amazing potential as a weapon. But if you try to do it as a mob of men against a force that understands how to push back properly you're not going to be very effective. The well trained armies likely understood this and this in large part explain how a smaller army could stand against a larger army. It's not just about how much force you have it's how you apply it. I think othismos and pulse are not mutually exclusive. People likely did actually physically push in combat but that style of combat would likely have created momentary lulls like men going back to the huddle.

Since you're already reading Adrian Goldsworthy, pick up his Roman Army at War, 100 BC - AD 200. It goes into greater depth and also analyzes battles in the manner of John Keegan's Face of Battle, systematically discussing infantry vs infantry, infantry vs cavalry, cavalry vs cavalry, etc.