>>39372800Gen 1-2 I don't think there was anything major removed. Then again, gen 1 was kinda barebones so Gen 2 just got to add everything it could.
Gen 2-3 though removed a couple major things.
Firslty, postgame. I mean, I don't know if people at the time expected another "let's do a second region" thing or not, but Ruby and Sapphire had way less of a postgame experience than Gold/Silver. Emerald fixed that a bit with the Battle Frontier, but I'm only talking about the first games in a generation here.
More importantly, and incredibly pertinent to now, Ruby and Sapphire removed transferring Pokemon from the old game to the new ones. This was due to technical limitations however, rather than a design decision like now. But it still happened and for a time there was no way to transfer your old mons up. They even retired the "Gotta Catch'em All" slogan at that time, only bringing it back in I think the 5th generation.