Stop bailing out the shareholders!
The main problem is that the US authorities consistently bail out the shareholders (and usually management too).
e.g. the US taxpayer only makes money on the spring Delta bailout if Delta shares went from $24 at the time of the bailout to $560.
If they created any amount of moral hazard (temporary nationalisation, recall of prior exec bonuses, cancelation of share options plans, and all of these do already happen in some segments of US business) then the airlines might save a bit more for a rainy day.
If you really believe that airlines are critical infrastructure then they should have government mandated minimum capital ratios like banks do.
But anyway, this is all wishful thinking, because the decision makers in Congress are all massive equity holders, so the above will never happen.