Otherwise, you do have a point, a systematic bank failure would likely cause issues here as well. However, I highly doubt they'd be storing significant amounts of money as cash deposits in banks for the interest. There's better options, such as short-term treasury bonds.
Storing serious amounts of money in any of these stablecoins for any real length of time is economically irrational because by exiting their walled garden, you can obtain a higher return in exchange for reduced risk. Withdrawing is even better than a risk-free reward; it's a risk-reducing reward.
My point is that bank deposits aren't as safe as people like to believe they are, at least beyond what is insured.
In a systemic crisis, chances are the government will just print whatever money needs to exist and bonds too will take a hit as a result. Plus, whatever happens in the US will impact the whole world. You can't realistically hedge against this with any currency/bond.