If we aren't paying the employees we currently have (and are thankfully, for the most part, still showing up for now) what makes someone think that we'd pay more employees to work (or that those employees would show up for) generally undesirable shifts.

ATC is already short staffed -- even if they were being properly paid right now you'd potentially have to move some of that finite resource from the current shifts to beef up overnight staffing -- at best only shifting the problem and at worst magnifying the problem as there would be fewer staff available to handle traffic during higher-demand periods.

You'd also in some cases be competing with freight/cargo traffic that generally moves on the backside of the clock to take advantage of those lulls.
And noise sensitive neighborhoods.