Equalizing ratings across rapid, blitz and bullet? I've been noticing that whenever I play rapid games at my current 2050 Lichess Elo my opponents are also between 1900-2100 blitz and sometimes their bullet rating is also sufficiently equal to their rapid/blitz rating. In my case , I'm stuck at 1750 blitz and 1750 bullet; I cannot seem to be able to increase these two ratings to that of my rapid rating.
So a question arises:

are there any benefits from equalizing one's ratings across blitz/rapid/bullet or is it sufficient to focus solely on rapid rating (as that is conventionally known to be the best way to improve at chess seriously) ?

I want to continue playing rapid and focus on slow tactical/strategic games, but it just feels weird that my blitz/bullet skills are disproportionally low when compared to my rapid rating, and it's weird that my opponents do not seem to have a similar problem.
Bullet and blitz are mostly for fun (especially bullet). You don't have to have the same rating in both bullet, blitz and rapid as not all the people can think that fast. Keep playing rapid games if you like them and remember that chess is a fun game.
If you (plan to) play seriously (participate in competitions), then you'll realise that rapid games are by far the most helpful because of the long time controls which allow you to think more and therefore make better moves.