There’s a theory that if there was such a bank, all money would flow to it making all of the other ones insolvent, in turn the financial system would collapse, since no bank has enough. The whole industry is just a house of cards.
There was actually a recent case where one bank (Custodia) tried to do this - they wanted to charge fees instead of gambling with their clients money. But the FED denied their application. They say it’s because they wanted to service crypto companies - but how would that even be a problem if they’ve always got all the deposits at hand. It smells fishy.