I hope someone who has a good answer replies here because I'm not totally sure.
But yeah, like you guessed, trading heavy pieces (like rooks) tends to highlight static advantages like pawn structure. Static meaning they're permanent features of the position. Material is another example. In contrast a dynamic advantage would be initiative.
Also in general there are sort of two principals working against each other... at least this is how I see it. The first one is pretty well known, and that's the idea of two weaknesses. You alternate creating threats which pulls the defender out of formation and lets you cash in on one of them. For this you want to keep pieces on the board.
The second is probably not as well known among amateurs, and that's zugzwang is ubiquitous in endgames. When the opponent gives up on counterplay and attempts a fortress, you almost always need zugzwang to break it down. This principal wants pieces to be traded off. Not only does that reduce their active play, but it's almost impossible to create zugzwang when your opponent has lots of pieces.
I'll say that in my experience (take it for what it's worth) there's usually a sweet spot. For example, in a given pawn structure maybe R vs R is a draw, and maybe B vs N is a draw, but R+B vs R+N is a win.
In other words you usually want to trade... but not too much... unless it's good to trade, in which case do that
But yeah, I'd say one of the biggest differences between, lets say 1500 and 2500 is that the 1500 almost always stays too long in the late middlegame, and / or rushes straight to single piece endgames. All the time you'll see strong players keeping 2 or 3 pieces, and fighting on and on in that phase, while lower rated players skip right over it.
Well, I've rambled enough. Hopefully I'm getting close to answering. Like I said at the beginning, I'd like to hear other's ideas on this too because I'm not completely sure.
All, Reading descriptions of endgame technique in complex endgames, I was struck by the high number of times step 1 or step 2 is "exchange a pair of rooks" (leaving only 1 pair on the board). Can someone with more experience comment on this? Is it a meta-rule? Is it's purpose mainly to reduce risk from possible counterplay? Or, .... Is it really true that 4 rook endgames are more likely drawn than 2 rook endgames?
Or is there a deeper reason or a reason more position specific?
Thanks for 'schoolin' me on this point! -Bill