Ultimately it falls on the taxpayer. The existence of the FDIC not only incentivizes but almost forces banks to be risky with their investments. It doesn’t matter if their lending fails because the government has to come in and clean it all up and those expenses are passed on to the public.
Banks aren't defaulting because they held bad PE loans. The recent memorable case was SVB, but it held quality paper, just with a duration risk. Banks aren't investing depositor funds in loans to Toys R Us.
Fractional reserve banking means the bank only has a small percentage of the money its customers deposit on hand (currently 0% since 2020). What do they do with the rest of that money? They invest it. They take on risky investments because it will either pay off or they will be bailed out by the taxpayer through FDIC. There is zero risk on the banks part.
Once you get as far as FDIC insurance being involved, the bank generally ceases to exist (ideally via a fire sale to another, more stable bank) and the shareholders generally get (all but) wiped out, at best.
Competent risk management so that doesn't (generally) happen is a core competency for a bank, and if regulators think you're doing it wrong they will come down on the bank's leadership like a ton of bricks.
If anybody reading this comment would like to learn more from people who understand the area far better than I do, I would recommend patio11's 'Bits About Money' and Matt Levine's 'Money Stuff.'
FDIC has as much to do with what you're talking about as the gravity that holds you down. Yes its technically correct that they're covered by both, but you're miles away from any kind of rational point.
