Another site I used to play on had the idea of day/move + a time bank to be used for additional thinking time or vacation. I think it is a good option.
Alternative time control for daily chess
A useful alternative to simply having 3 days per move would be a long time control like 30 moves in 30 days where your clock counts down whenever it is your turn, so essentially 30 moves in 720 hours. They could also impose a maximum of 3 days for any specific move.
If I play in a regular chess game with 40 moves in 1 hour, say, I could use 39 minutes over one move if I like, and play the other 39 moves bullet. It might not be the best use of the clock, but I wouldn't lose the game on time that way.
It could also work with an increment. So you start with 3 days and a 1 day increment on each move you play. But again, a maximum of 3 days for any specific move.
All these ideas seem worthy of investigation. I would also say that chess.com has a very liberal vacation policy, and I think it is abused too often.
In my opinion, the best time control for daily chess would work like this. Start with 3 days on the clock. After every move, carry over unused time and add 3 additional days. Have a cap so that a player cannot use any more than 10 days on a single move without using vacation time, although they still keep all unused time even if it is more than 10 days. Also, have a limit of 30 months for any daily game.
This would provide an incentive to move faster when there is little to think about, especially in the opening. The average time per move would always be under 3 days unless vacation time is used. 3 days per move seems to be the most popular time control for daily chess now.
The USCF uses the following time control for daily (correspondence) chess. Players have 30 days per 10 moves. If a player plans to use more than 10 days for a single move he needs to alert his opponent. There is a limit of 30 months for each game, and there is no vacation time.
The most common time control for daily chess in team matches and tournaments seems to be the chess.com default of 3 days per move. In most cases, this works reasonably well. However, incidentally games become very slow when both players always use their full three days (and perhaps even add vacancy time to it). This is particularly irritating in tournaments when occasionally virtually everyone is waiting for the next round to be started. Then only a single game might still be running, lagging the others by more than a month. The same is the case (but less severe) in team matches whose status is often 99% for months before finally the last game is finished.
What about implementing the following version of the Bronstein time control as an option for daily chess: Each player has a certain time (say, 1 day) per move plus a buffer (say, 30 days) for the whole game in case he exceeds the move time for any of the individual moves. I would love to have this "1 day per move + 30 days buffer" time control for the tournaments and team matches I participate in. This would limit the possible length of a game to [2 * (number of moves + 30)] days -- still a lot, but extreme delay would be prevented.
Incidentally, this time control would also solve the "Sabbath problem"