It should be blitz like 3+0. It is very similar time.
It is completely different game from 1+0.
I agree that is completely different to 1 + 0 time control. But it still requires speed because you can't think for excessively long.
You can have a look here for how time controls are decided:
lichess.org/faq#time-controls.
3+0 is the fastest Blitz control. 2+1 is slightly faster (by the 40-move-rule), hence it's Bullet. Granted, if you're in a long endgame, then 2+1 can be easier to deal with. But there's also little 2+1 tournaments.
Not only are you right this should be taken further. In the era we find ourselves in chess wise it is more important than ever to distinguish this 1 minute rating.
I agree with the logic that 2-1 is to fast to really be proper blitz, but I think it is more appt to be called blitz than bullet.
OTB 3+2 is called blitz, but you have to press clock each move what consumes time and you can't premove. For me ONLINE 2+1 is similar to OTB 3+2.
So I suggest to change 2+1 to blitz or maybe replace 2+1 with 1+1 and leaving it as bullet.
2+1, aka correspondence bullet, is the only way snails like me even can have a bullet rating above the technical minimum. Keep it!
I like the term pensonist bullet, or "Rentnerbullet".
@fuxia "This player uses fine Riesling assistance". I never heard of that engine... =)
lichess qualifies X+Y time control according to X+Y*40/60
FIDE qualifies X+Y time control according to X+Y
I think before making 2+1 a blitz-time-control, 3+0 should be made a bullet-time-control, cause it doesnt have much to do with blitz and is on lichess much more based on "how fast could you make good pre-moves".