I'm going back to endgame basics right now (a seriously neglected part of my game), and I'm finding that having to figure out how to play some of these endgames does wonders for my entire chess understanding.
Honestly, I could tell you the same thing from openings, that it helped the understanding of the entire game (yes, even endgames). Every opening has a different philosophy or strategy and of course most of the time these strategies have many layers to them. The french is about pawn chains, closed positions, wing play, and central play too. The QG is about trying to get a superiority in the center, or for white, maybe to open the c file at the right moment. The nimzo indian to indirectly put pressure on the center and to exchange bishop for knight to get more control of the center (since the c3 knight controlled e4 and d5) and in many cases work against the doubled pawns by closing the positions, thus making the knights better. The list just goes on, and on, and on.
Like I said, I think the endgame is important, perhaps more so than openings, but it seems that learning it only helped with endgames, and being able to keep in mind if in a middlegame position will I have a favorable endgame if pieces trade off. I'm just saying learning opening strategy has its merits, and it's helped me so much.
Your statement is so logical, that I'm really mixed up. What you said about your opponent being messed up coming into the late middlegame and endgame because he may not know the openings like you do; well, Josh Waitzkin said that when he played in tournaments in his teens, he was never good with the openings, and would always go into the middlegame down 2 or 3 points because he played opponents who only studied opening traps, and so they were helpless when they played him in the middlegame and endgame, and he ended up always beating them.
Yeah I know Waitzkin said that but I'm pretty sure that he was playing too weak opponents in those tournaments. I'm only a class C player and I have never lost a game where I ended one pawn up from the opening in a long timed tournament game. There mostly is no simple recovery from compensationless pawn losses even at lower levels, unless you're playing blitz chess. Ofc this is mostly only true if you face an opponent of your own strength. A GM that somehow would lose a pawn against me would simply crush me after 10-15 moves anyway. so what I'm saying is that Josh was either trying to make a point for sake of it (because endgames are important too) or he was lazy and really didn't study openings which is dumb imo.
As I said, study both and you'll improve faster and if you are trying to pick one of them to start off with just go with your gut and start with the one you think is more fun and then do the other.