Furthermore I'd argue that insuring deposit banks through the asset-limited FDIC is yet another setup to socialize catastrophic losses. If bank deposits were guaranteed by the Fed directly, the Fed could print an unlimited number of dollars to make depositors whole, thus completely eliminating the risk that a USD-denominated deposit simply vanished. (The realized damage would instead be expressed as monetary inflation)
The FDIC is backed by the full faith and credit of the United States. It legally cannot run out of money.
Its fees are mostly an accountability mechanism on the bureaucracy. If the FDIC burns through its reserves and has to ask the Treasury for money, it failed at risk management. Some folks may get fired. But the bills will be paid.
The FDIC is legally backed by the full faith and credit of the United States, its liabilities beyond its own resources, to the extent that such may exist, are debts of the United States.
Which has a fundamental power to mint US currency, and thus cannot meaningfully “run out” of it.
I believe risk can be moved around, but it can't be eliminated. This is probably fairly mainstream Wall Street analysis, too. I also believe that all attempts to move around risk must also increase it on the net, e.g., if you do the extremely popular financial move of taking a modest chance of modest loss and stuffing all the risk into a small chance of total loss and then hoping that just never happens, that the total risk has increased. This is probably less mathematically provable, and depends on a lot of assumptions about how one compares various classes of risks. (I base my thinking on a variant of what you might call the "more or less efficient market hypothesis"; if there was a way to net reduce risk overall, it would probably already have been taken.)
The bank abstraction you refer to is in my opinion in that class of "extremely popular financial moves". Yes, it removes the modest risk of partial loss, but it moves the risk entirely into a small chance of total loss when the entire system comes down instead. I worry about the net effect of millions of little financial transaction that all perform that particular risk management move. It ends up creating a lot of easily-hidden correlations in the system, and no one entity (let alone person) can have a view of the whole situation.
In the end, the risk is moved around, but the bank run is still a possibility and no amount of financial abstraction can truly remove the fact that the liquidity term mismatch is a fundamental aspect of such an operation that can't be erased, only managed.