Playing on other websites or in real world, we usually see these three different time controls or their combinations:
--> Time for a whole player's game
--> Time increment per move
--> Time buffer for a move.
About the third one, there are two variations, either you are forced to move within allocated time (like 1 minute per move versus AlphaZero?) or where the time for a game doesn't start to run, unless you go over the time buffer, like in 4-players chess on
www.chess.com (X seconds for a move, and only after this the time for a game starts to run away).
Maybe lichess could have all 3 types of time control too?
Time buffer is very nice and useful, as you can always move within these few seconds, without worrying about losing any time. It's fundamentally different from time increments, as this time is independent and it doesn't stack, so you could play for example ¼+0 or ⅛+0 with 1 second per move buffer, without losing any time at all, unless you go over this 1 second!
I think that it could be really interesting option, especially for a bullet, which could also be used for other purposes, like as recompensation for a lag or for long time controls to reduce time increments and make games shorter, while still allowing for a quick moves in the endgame.
This way you could even play 0+0 games, with only condition being that every move would must to me made within the time allocated, for example within this 1 or 2 seconds :-)