I mean, if people run, the bank or credit union will fail. But people are fundamentally lazy and there's not much of a difference between getting your money on thursday and the next monday, so there's less urgency. People are also fundamentally panicy too, so I agree there's still a risk.
Stock market 'circuit breakers' that halt trading when the stock moves too fast seem to be pretty helpful. Maybe banks need something that halts withdrawals when they reach 10% of last reported deposits. (Spit ball: each depositor may withdrawal at least 10% of their current balance or last two statement balances, whichever is more, any excess is allocated on a dollar basis across the day's withdrawal requests. Some mechanism to pre-request funds so you can be sure you can wire large payments for houses, etc)