The problems that the airlines are having relates to their lack of caution and foresight. Stock buybacks are great as long as you have the cash--unless there's a recession, in which case you're short of cash due to decreased business, and you find that if you sell back that stock, you take a loss.
So should we spend taxpayer dollars to save them from their mistakes?
My solution is that the government buys all that extra common stock. The airlines can have the option to buy it back after X period of time. This way, it's not a giveaway--essentially, it's a loan, with collateral.
That, the public might find palatable. A direct goody giveaway, not so much.