It's surprisingly handy to have the ingame clock match up with the time used for events. That way you can see, at a glance, how close you are to something that might be going on.
I think the best idea would be for people to change the time locally. (So they can choose what the time should be from their view, whenever they want. I remember another game having a feature like that)

You can already do that in game. Right click the clock in-game to open a menu and click on "use local time".