The problem was clearing house margins. It went from a few percentage points every buy of GME to 100%. You cannot use customer money for these deposits, it must come from the brokerage firm's funds itself.
I think it really needs to be discussed that there were multiple "liquidity" crunches for RH here, one far more significant than the other.
You could have had every single buyer of GME locked and loaded with $100k of cash in their account for a month, but if they all bought GME last week for cash RH would still have the same exact margin requirement problem they have now with their clearing house. That they still had hundreds of billions of their customer's capital on deposit would have been irrelevant.