It depends on how you define "chess."
Any time variant changes the game completely. The longer the time frame (generally) the more accurate you have to be in order to win.
The exception to that rule comes when you play longer time frames in the same categories. Bullet has 1|0 2|1 and something else, blitz has 3|0 5|0 and 5|3 I think and rapid had 10|0 to like 30|0. The longer you go in the same category, it seems the lower skill level of the opponent except maybe rapid for the higher levels.
That said in any given situation, when there is 10% of the time left or less on either player's clock the need for accuracy is trumped by the need for speed. Sometimes accuracy becomes exponentially more important in those scenarios if there is say a mate in 4 or less. Otherwise, if you're playing bullet, and you both have five seconds left, no mate in sight, it may be best to sac your pieces to check your opponent or prevent the move you think they'll do so they have to take more time provided you can find the move instantly. If you take more than a split second on calculation, it's too much.
Are time increments a benefit or detriment to chess improvement? They seem to be a bit of a safety net.