The key difference is that Robinhood isn't a bank. Bank runs are bad because banks are assumed to be massively liquid---in the average case, if you walk in and provide the proper ID, they can hand you the cash you're asking for. If they can't, one of their primary value propositions is at risk and people start demanding their money out because the bank isn't able to provide the services of a bank.

This is not (and is not expected to be) true of stock brokerage. Nobody generally has an expectation of moment-to-moment liquidity (or even closure of deals), even in a stock with significant availability. However, a brokerage deciding independently "You're not allowed to buy this one stock" is unusual, and can cause people to start backing towards the exits.