This is why I propose zones. If I'm in zone A stealing from a vault in real-time and you're in zone B sleeping you can't interact with my zone until I'm done. Better yet, a "virtual GM" would give you something to occupy yourself with until I'm done.

I can still see problems with that.

Imagine a group of characters going into a large dungeon and then deciding to split up to cover more ground and/or not get in each others' way in the narrow corridors. If one group decides to sleep, but the other stays awake as they encounter more enemies, it wouldn't be very practical to force the first group to stay put until the other sleeps too.

It seems to me that this system would encourage players to delay sleeping and discourage any form of friendly competition (as in one group saying, "I bet we get there before you guys").

I see what you mean. I think that including sleep is going to require a fairly flexible system that can summarize and abstract the day's events in order to keep a good sense of pacing. Whatever you do I don't think you have the option of playing out events second by second at all times and letting players sleep informally. Without abstraction you're going to have to resort to other (maybe more familiar) devices like having players "sleep" for an unrealistically short time or cast a spell or something unless sleep / training / etc. is anything but idle time.

Is it possible to synch the players so that, no matter what, they need rest at approximately the same time?

with up to about 16 players in the same world

How many of them will be online when you login? If they live in different timezones and each play for 2 hours a day then statisticly you can meet only 1 fellow player... I don't see it working for an RPG. For turn based strategy, no problem, but realtime RPG with its social interaction...

Is it possible to synch the players so that, no matter what, they need rest at approximately the same time?

I think most players would accept their level of fatigue being affected by a lack of sleep/rest and there being a point where that would incapacitate their character. However, they would also expect that to vary depending on their character's stats, and how active they had been.

I suppose each character could be defined as more/less alert at night during the creation process and/or by their actions, with appropriate bonuses and penalties when doing tasks.

How many of them will be online when you login? If they live in different timezones and each play for 2 hours a day then statisticly you can meet only 1 fellow player... I don't see it working for an RPG. For turn based strategy, no problem, but realtime RPG with its social interaction...

The idea is to allow people who want to, to play with a few others without hundreds of strangers being there too (as there are in MMORPGs). Most of them will probably already know each other to some extent.

It shouldn't be too difficult to provide a method of finding other players who are online at similar times so they can meet in the same game.

It worked for Diablo and Neverwinter Nights.