Your right; that's why I don't do much business with large banks ;).
I have one account with a large bank. I have not had any problems, but I limit my transactions with them to well documented transfers and have standing orders to not allow any other type of transactions.
I have no expectation that a large bank will cover my liability better than they cover theirs. I engage with them accordingly.
The best way to spread your risk with banks is to make sure you never have more than your federally insured cap with any one bank. (that's a luxury problem though). Over that and you're up the creek without a paddle if anything should happen to that bank.
The funny thing here is that the people that the bank owes money over that amount are ruthlessly culled, but the people that owe the bank are not.
I think that should cut both ways, in other words if a bank folds then both the debts and the deposits should be capped or none. But it seems to be completely asymmetrical to keep the people that owe the bank on the hook while capping those with whom the bank is in debt.
I have one account with a large bank. I have not had any problems, but I limit my transactions with them to well documented transfers and have standing orders to not allow any other type of transactions.
I have no expectation that a large bank will cover my liability better than they cover theirs. I engage with them accordingly.