If something happened that a big broker became insolvent and investors weren't able to access the markets, the contagion would be catastrophic. Worst than the financial crisis and Lehman. The Feds would be quick to step in. Imagine the panic when a headline crosses that something happened at TD Ameritrade that may leave investors with no access to the market or their money, that there may be bankruptcy.
I can't imagine how the customer wouldn't be able to just transfer their holdings to another broker. There would have to be some real shady stuff happening. Like Robinhood