You can give free money to the banks, or you could give free money to everyone else assuming some of that money would be deposited in banks and/or used to pay down debt owed to those banks. You could also, say, just add $10,000 to all the bank accounts, giving the banks more reserves and many people more cash.
The point is, if you're handing out free money to save the banks you can do it in a way that saves the rest of us, too.