Could a global government, like the UN, build a server that would handle all the transactions, thereby making it impossible for private servers to turn a profit?
So in the future, will bitcoin mining become so sophisticated that only a centralized entity will be able to handle it?
So you want bitcoin to evolve to have centralized control by a few very wealthy countries (that's largely what the UN is). That sounds like a very sad end game for Bitcoin, but maybe the UN (and only a united organization of all nations) could be responsible enough to not fuck it up. For right now, I much prefer this thing in the hands of millions of ordinary people and businesses a like.
The reason Segwit2x failed is because the SMALL INDEPENDENT miners refused to adopt the new code. So your worries about centralized private mining have not come true and in fact took a serious blow from all the independent private miners.
I think it's best that this thing remain out of the control or influence of any government. Governments, inherently lie, cheat, and steal when forced to do so. There's no real negative consequence for a government to limit that kind of bad behavior under what they deem are "urgent circumstances".
And, yes, it would be possible for a server (or several servers) to handle all of the transactions.