In addition to the mentioned issues with TSA staffing, ground ops personnel, DL agents, etc, there becomes a significant issue with flight crew duty and rest rules. Once one starts to operate within the window of circadian low, different rules come into play (reduced block and duty times, limitations on the number days one can operate consecutively in this window, etc). These rules are carefully accounted for in bidding monthly schedules, but to just randomly start incorporating these into already planned schedules would be a crew scheduling nightmare (not to mention unions would - rightfully - have a field day with this).

So while it’s a neat thought, I can only see this being viable if the shutdown extends another month or two. Hopefully not.