The purpose of a clearinghouse is to manage that counterparty risk prior to settlement, and ensure that settlement occurs smoothly. Some clearinghouses like OCC carry counterparty risk throughout the life of a trade.
The counterparty in question is the clearing member, ie Robinhood. If the trade is fully cash-secured then there is no risk that Robinhood will go under because it has 100% of the cash required to make good on the trade (assuming they still make enough from PFOF to cover their operating costs for a couple of days.) And for existing margin accounts, they just have to continue the practice of aggressively closing positions that fall below maintenance margin.
The NSCC formulas for this (I assume these are the relevant ones and if not that they're representative) are published. You can just go read them. I don't see where they say "if trades are made with customer cash and not on margin you don't have to account for them in the equity group collateral requirement". That also wouldn't make much sense; the clearinghouse protects participating firms from each other, not just from their customers.
Actually, the Clearing Fund Formula accounts for Margin Requirement Differential, so margin is indeed a component of the amount posted.
More importantly, cash requirement effectively reduces the amount of leverage that customers are able to use, and that means (A) no additional firm capital needs to be lent for purchases of GME or whatever other stock, and (B) margin-account customers trade less on a given amount of their own capital.
Are you suggesting that Robinhood would be required by Procedure XV to post more than $1 for every $1 of GME stock that a customer buys in a cash account?
I'm not sure I follow why the future actions of Robinhood customers matter. They've executed the number of trades they've executed, DTCC raises the collateral requirement for meme stocks, and now they're on the hook, whether stocks were purchased on margin (implicitly or otherwise) or not. You've got the rules in front of you. They seem to plainly say that Robinhood has to put up collateral regardless of whether margin is involved.
Again, I think the margin stuff is mostly a red herring?
The counterparty in question is the clearing member, ie Robinhood. If the trade is fully cash-secured then there is no risk that Robinhood will go under because it has 100% of the cash required to make good on the trade (assuming they still make enough from PFOF to cover their operating costs for a couple of days.) And for existing margin accounts, they just have to continue the practice of aggressively closing positions that fall below maintenance margin.