Yes, my 2yo DS definitely plays more with his toys since we streamlined them about 9mos ago. He still isn't big on toys but it's way better than before when everything was completely ignored! We don't keep toys DS doesn't play with, and we don't keep noisy plastic toys or toys with very limited use. It's hard especially to get rid of gifts but it's for DS's sanity (and mine as well!) so I just do it (and I've told everyone what kinds of toys we prefer for him, so if they totally disregard that & get him a noisy plastic robot that he is absolutely terrified of, I have fewer qualms about returning/donating it right away!! Plus I suspect they aggravate DS's sensory issues.)
Having the toys organized is huge... It actually makes it look like we don't have many toys -- and it's true that we probably have fewer than most do -- but there are a lot still, it just doesn't look like it. Most of the toys have spots on certain shelves amongst the books, and we group similar types of toys together, so there is a basket of play pots/pans/food that he'll take out & play with & then put away, and a basket of little animals, a stack of puzzles, a basket of musical instruments... He likes keeping it all neat and although a few toys get strewn around at times (mostly when DH is playing with him

) for the most part it stays pretty tidy. In fact DS has been home all afternoon & evening and the only things on the ground right now are a little doll, 2 magnetic letters from the fridge, and his hockey stick.
OH and DS has a 'bedroom' upstairs (has no bed in it since he sleeps in ours still!) that we are using as an occasional playroom. The upstairs is gated off due to construction, so he only goes up there a couple times a week, if that. Many of the overflow toys (the ones I'm not ready to get rid of but don't want out in the main part of the house) go up there and they seem more 'new' to him since he doesn't see them often. This was our alternative to rotating toys (which for some reason seemed stressful to me!)
So yeah, I absolutely 100% recommend streamlining as much as you can and setting up some kind of rotation with what remains so there aren't so many toys out. Just start by getting rid of things that are broken or annoying... those are the easiest to part with, and kind of get you in the groove. Also, I've made a good amount of money selling stuff on CL which is a great side benefit lol!