A 3000 could easily beat a 2000, but could a 4000 easily beat a 3000?

Yes

Meh still 4000 clap 3ks cheeks

Don't forget it's a 1k mod

ofc he she could, I've beaten 2'500s often and I'm 5hundred something.

So I wouldn't let it strain your minds too much, I've just answered and solved the mystery for you all. : )))

2,500s or two 500s?

Hikaru is 3440 in Bullet what the...

He is very good at it. Has trouble against Magnus when it matters though.

Due to the 150 point inflation IIRC

No. As time controls get shorter, the bell curve gets wider. It turns out that a weaker player has a better chance of holding their own when each player has more time. Thus the top of the bullet rating graph is higher than that of the standard time controls graph (say FIDE) and the top of the unassisted correspondence chess rating graph is lower. 

Of course, it is also important to align the ratings at some point such as the median, but that is a separate issue, no way explaining the difference between 3400 and 2800 (rough top of the two distributions).

Exactly why the 50 move rule should not exist. Instead, of two players are frolicking around in a drawish position, have the arbiter just declare that if the game does not end in a half hour after the 50th move, it's a draw. If the grandmaster could play out the 200 moves speedy fast in bullet style, who cares if it goes beyond 50? It's about wasting time, not moves.

Are you more referring to the Interquartile range?

The variance, standard deviation, interquartile range - all of these are larger on the wider bell-shaped curve of bullet ratings. (The lower end of the distribution likely gets truncated, because a lot of players are perfectly well aware there is no point in playing bullet because they cannot find moves that are even mostly passable quickly enough. If a player finds blitz too fast, they likely won't  bother with bullet).

With increments, total time is less meaningful, that's one substitute for the 50 move rule, get rid of the increments.

I agree, because the number of chess games in finite, ratings aren't.

That's crucially flawed reasoning: it can be a lot quicker to mate if the defending player errs.

Nonsense. The (integer) ratings between 3000 and 3000000000 are also finite, and minuscule compared with the number of chess games.

It takes 232 moves if the Nalimov EGTB plays itself. That is not to say that a human who has studied the endgame couldn't mate against a human who hasn't in considerably less.

Also, if Troitzky could accurately analyse wins in 115 in KNNKP before computers were constructed, it's questionable that no human could ever solve the position shown. 

Whether a human would ever find that or not is irrelevant to the rules of the game. Winning positions shouldn't be declared a draw on a technicality other than time.

Exactly, and as you said,  the hundreds of moves is only if both sides play perfectly. Now, both sides not playing perfectly could cancel out, also taking hundreds of moves, but as long as one player can see slightly further ahead than his opponent, he may definitely find the shorter wins resulting from non-perfect play.