See this essay on why living without time zones is probably a bad idea:
https://qntm.org/abolishHaving no time zones would probably work if you were geographically restricted to one area (as will probably be true on Mars for some time), but when you get to the point where you're covering a large enough part of the planet, you're going to need them, even on Mars.
I also think you'll find that no matter what you do you it won't be long until people start being fuzzy with how thye express dates and times.