So the options are:
1. Banks eat the cost.
2. Banks take on more risk to cover the cost (putting the whole system at more risk).
3. Banks increase customer fees, interest rates, etc...
I don't have a crystal ball but I have a strong guess about which of these options are most likely to be implemented.
Not only will tax payers likely pay for this but the most likely tax payers to pay are the ones with the least flexibility (stuck with variable rate debt, limited banking choices, no dedicated money managers working on their behalf) aka the poorest tax payers.
If my assessment is correct, they have somehow found and settled on a solution more disgusting than a generally distributed tax payer bailout.
The Fed releases a digital dollar that you can bank without needing to be a part of this oligopoly. Banks are forced to give better terms to be attractive again, terms that will make up for the risk of the bank using your money. Deposits are no longer guaranteed because being in a bank is now a deliberate choice instead of something you're forced to do despite having money.
Banking is not competitive in any way. The small players are very risky to bank at. The big players get to be riskier because they are protected by the government.
That's not a given since it may just reduce profits. Banking is a very competitive environment.