If you think New Yorkers don't need the subway after 9am or at night, you're deeply mistaken.
Well that isn't the suggestion; the L is obviously busiest during rush hour.
During the day would be disastrous, but doing as much work as possible from 1-5am (on a line at a time, not all of them) might work. Ridership and road traffic is low enough at that time to make replacement with buses feasible.
London does this, IIRC.
Yep, and it's mostly a non-issue. It might take you a little longer to travel at that time, but there are buses that will get you anywhere you need to go (and it's partly mitigated by the fact that the roads are empty at that time of night).