Maybe so. But the flip side of that is that (IMO) a bank that qualifies for FDIC insurance on any sort of scale should have to follow the same risk-controlling rules (Basel III, etc) as any other large bank.
The government has a strong interest in making money be money — someone who holds USD and uses it for transactions should be able to be confident that it won’t evaporate. Currently, one does so in an FDIC-insured bank or by purchasing short-dated [0] treasuries.
And if the government backs a guarantee like this, it should exercise a corresponding amount of control over what becomes of that money.
[0] Hey SVB, you forgot the short-dated part.