Always struggling with time

I really hate time pressure, should I give up rapid and blitz and bullet forever? My classical rating is 2000, with tight time control and no increment I can't even defeat 1700. I can't imagine how people play under such time stress, I think it's very bad for mental health.

Some people just work different, and some of them maybe doesn't have that much free time for classical chess, so they choose faster variants

I play my best when I focus on one time control. I was struggling to hit 2200 in Rapid. I stopped playing other time controls (with a few exceptions) and now I almost hit 2300 in Rapid. I think this is mainly due to improved time management. I get in time trouble some times (and lose some points due to it) but I think this is fine. My brother who doesnt play so much says also 10+0 is too fast for him, so he plays 15+10.

same rating on different pool does not mean same skill level. Rating system does not measure you chess skill but how much gain points against opposition. And very few strong people play classical which result median player i.e 1500 to lot weaker in classical pool than in rapid. Also classical suffer more than rapid randomness due to people playing at blitz speed regardless of the clock

Since there are allway lots of new players median of each pool gravitates 1500

www.reddit.com/r/lichess/comments/mdvbkp/yet_another_lichess_vs_fide_rating_comparison/
from thre you can how different formulas predict the fide rating from different pools. Also that show that correlation to fide strengrh if really weak -> correlation from one lichess pool to another is very weak

Time plays a vital role in the game.Every player struggles in the early days of his career and its totally acceptable but if you want to play the game with seasoned players then you have to start adapting to play under pressure.I know clock just adds the pressure on players but it is a part of the game you have to get used to.I strongly believe if you are able to master this aspect of the game wisely then it could become your greatest weapon.
My personal advice is to cultivate the habit of looking for forced moves and work on increasing your speed and accuracy.
Play as much as you can, nothing can beat experience!