To solve your "what about moment-to-moment gameplay where one player can enter a turn-based battle in an area while others are roaming freely?" objection:
-You could also have time pass according to the host's clock. If the host is in combat, the clock is frozen for everyone (like how the game currently works). If the host isn't in combat, time passes.
I find this approach too prone to break things.
Imagine a turn-based battle for one of the other players dragging beyond the point where the host (playing in real time) is already experiencing the swap between day and night and I guess you'll see why it could turn into a mess quickly.
Then again, I'll stress that this isn't a big deal at all.. Extending the day's length by a bit because the clock is paused doesn't cause anyone real troubles... And frankly how often and for how long will players involve themselves in lengthy and complex battles without having the other players participating in any way, shape or form?