When it comes to "fights give momentum." Removing the CTE/injury issue from it all.
Taking it as true that we can point to instances where a team was losing, they won a fight and then they united, rallied and won, and that it's not even a point of contention that a fight changed the game... ok. In any sport involving an offense and defense, there's two sides to the same coin, and everything that occurs is a net zero. If one offense is suceeding, the other defense is not succeeding, if one side has momentum, the other side does not have momentum. So then, logically, it has to be the case that the other side would say that they lost momentum as a result of the fight, and that they would claim, as a matter of it not being a point of contention, that the lost fight resulted in them losing the game.
With something like "momentum", it can be gained or lost in a number of different ways. Taking fights as a for-granted way to gain momentum without directly effecting the scoresheet, you can also add things prolonged offensive zone time, big hits, great saves by a goaltender, etc. How does fighting differ from each of these? The idea of consent. Teams don't "choose" to let the other team have prolonged zone time, they don't choose to be on the receiving end of big hits, they don't choose to have the goaltender make great saves.
With a fight though, they do choose. It takes two willing participants to participate in a scrap. Of course, they may not know who will win the fight beforehand. However, in general, over time, one side can theoretically realize if they have an advantage/disadvantage in a fight. Think about this in other contexts, if your team is not well suited to a style of play that is wide open, trade chances for chances up and down hockey... you tighten things up. If the low scoring, tight checking doesn't suit your team well, you try to open things up and catch the other team in more free-flowing situations. Essentially, you make adjustments. If your team is bad at fighting, this costs you momentum and ultimately results in you losing games, the natural adjustment to make it is... if you are running your team optimally, stop fighting. It's completely within your power to consciously not provide the other team this advantage. Probably more so than any of the others, the other team can try and push/slow down a pace. They cannot force you to fight.
This connects with the other thing that fighting MUST be voluntary. The other team cannot adjust to your adjustment by essentially jumping your team to gain the advantage seeking fight. If fighting is not voluntary, it removes all logic of two consenting participants choosing to partake in an activity and accept the risks that come with it. Anything else is removing the voluntary assumption of risk that makes fighting have any moral justification as a place within the game. So if one side wants to fight, the other side does not want to fight, there can be no fight. So the side with the advantage in a fight should never have an opportunity to realize their advantage unless the other side consciously make an unforced error in choosing to fight.
TLDR of this this; if fighting does in fact give momentum the winning side, the game theory optimal move is for one side to just never fight, and thus fights should almost never occur.