There's been talk before of shorter time controls for the online chess section, but I believe the idea is for it to remain a correspondance-style match where nobody is ever required to do more than log on once per day and make their moves.
That's why there's Live Chess with just about any short time control you can think up being played at any given time.
So far as people not resigning, it's poor sportsmanship but not totally against the rules. Since they're technically allowed to use all the time, it's up to them if they want to delay by waiting the maximum amount between moves. There is a slight exception there. If someone is constantly using their allotted vacation time to delay an obviously losing game to stave off rating loss, that behaviour is against the rules and can be reported to the site.
I'm new to this site, but I think a 12 hour option for online games would improve things a lot. On a related note, what is the ettiquiette of a player simply not moving when the game is lost but he/she won't resign, running out the clock in a way. It's like watching paint dry. I believe an opponent of mine is doing this. I assume he'll get a loss but still, . . .