There have been "hardcore" tournaments with 0 timeout games that only had timebank, but as far as I know that has never been offered as an option with regular games here.
You could always go to the "site ideas" forum and make a suggestion, and see how it goes. It might make an interesting change. Maybe members who have played any of the "hardcore" tournament games could let us know how they liked it.
I think the reason that we can't offer zero time is the timezone factor. If timezone differences are involved it can be extremely unfair to one of the players. Say I'm an hour ahead of you, we each make one move per day at the same time, so each move you use up 1 hour and I use up 23 hours. All you have to do is make sure you last for a reasonable number of moves and you get a timeout win! So, 1 day per move is the minimum for fairness because provided you make 1 move sometime during that day you won't use any of your reserve time.
Blitz doesn't have that problem because you're both playing at the same time and both clocks start at the same time.
But you can move after me, i.e. 12 hours after. If I don't use time to think better for me, but, normally, I'll need it.
I understand the problem is to have to be conected frequently for don't using up more time of that you need for thinking the next move . Players should make several moves each day and assume use up several hours of their tomebank.
It would great if clock could stop for sleeping. May be, I'm dreaming.