Well, that's not quite true. There is always a small risk of losing some (or even all) of your money, particularly if you have a large amount in your account. Obviously that risk is very, very low for smaller amounts of money.

There are risks we should be concerned about, and risks we should not be concerned about. If you stuff money under your matress, the risk of losing it to a house fire or robbery are several orders of magnitude greater than losing it in a bank run.

Assuming your account is under the FDIC limit, how could you lose money on an insured account? Suppose there's a massive bank run and the Fed has to print oodles of cash to repay depositors. This leads to runaway inflation that occurs over a very short period. If you could have otherwise exchanged your cash on hand for a different currency, sure you would have lost money.

Compared with the actual risks of being unbanked, this is a hallucinatory concern.

250k is the insured limit. You can open accounts in multiple banks if you have more cash than that.