My emotional brain thinks we should just give up and climb back into the trees.

Funny enough, a story just broke about a lunar timezone, which would lose a second or so every year relative to Earth due to relativity. If space travel becomes a big thing we're going to have to choose a frame of reference, and probably just go with Unix epoch in that frame as the universal time. Hopefully it doesn't happen to pass through a black hole, because there's no consistent way to define a frame of reference that's not subject to gravity.