Hahaha... Maybe. Call me when someone gets to 4000.
A 3000 could easily beat a 2000, but could a 4000 easily beat a 3000?

At 3000+ engines level , draw rate is more than 90%, At 3300+, full destkop haradware (let us say 16-32 cores ) stockfish vs stockfish, Komodo, Houdini in standard games, drawrate is beyond 95%. So computer programmmers from talkchess forum estimated that, the rating of perfect engine will be between 3500-4500. Remember , chess is a verydrawish game, and an engine with 500 rating diffference can draw another higher engine very freqnently and the rating of higher engine will drop very significantly.

I think my question is perfectly reasonable. At a certain point, the players are so good that no matter what the difference in rating is, the game will be very hard.

I totally agree, at a certain level chess is nothing but a draw. A win in chess is based on your opponents mistakes which you must punish. No mistakes, no win!!!! Nothing but a dead draw!!!

I mean the only advantage white has in the opening is because he has the initiative and more or less dictates the pace of the game. With perfect play, this advantage gets liquidated in the middle game, always.

Depends who is white. Computers make mistakes. The most recent top computer game featured a win.https://chess24.com/en/watch/live-tournaments/tcec-2017-stage-2/14/1/2. In my opinion, a top engine won't reach 4000 by itself. There has to be a new era where new engines crush the current ones and get ~3600, then the top engine of this new group might get close to 4000. In our current state, it might take decades. Answering the OP if an engine gets 4000, that means it consistently beats 3000+ or else it can't get to 4000 in the first place. Thus, a 4000 rated engine would crush a 3000 rated engine. Whether a computer ever gets to 4000 is a different question.
Yes, the 4000 would crush the 3000 just like a 2000 crushes a 1000. ELOs are relative, so if the 3000 ELO was a perfect player and couldn't be beaten, then noone could attain 4000 ELO.

Yes, the 4000 would crush the 3000 just like a 2000 crushes a 1000. ELOs are relative, so if the 3000 ELO was a perfect player and couldn't be beaten, then noone could attain 4000 ELO.
When a rating gets 3000 and above, it's all the same right? A 10,000 vs a 3000 would be a challenge.