Pretty much everything you wrote is incorrect. You are describing margin lending, which had nothing to do with the issue. Robinhood instead blocked trading even for fully funded accounts. The problem wasn't the money that Robinhood lent you, but rather the fact that they themselves didn't have enough collateral to get cleared for the increased risk posed by these stocks. They were posing as a first-class brokerage without having the financial backing for it.
Moreover, the issue brought their business model into public spotlight, and people realized the problems with making money by selling order flows and the conflicts of interest that came with it.
My understanding is most people aren't commenting on this coherently†. The problem that halted Robinhood's GME trades, as I understand it, was that they had insufficient collateral to cover their clearing requirements. Clearing collateral isn't customer money; it's funds that clearinghouses require brokerages to post to protect them from each other. This, as I understand it, is money Robinhood was required to have on hand regardless of whether they had the money from customers to back trades. The amount is based in large part on the volatility of the stocks they're trading, and papers the illusion that stocks trade instantly when in fact the actual trade takes days to settle, during which the price of a volatile stock can swing wildly.
My understanding is that nothing you can do with customer trading funds will mitigate or offset your clearing collateral requirements. Brokerages that want to clear trades just have to have a big chunk of segregated money set aside to keep participating in the market. Robinhood ran out.
† because it's complicated, and there are lots of simple explanations you can come up with that are wrong, and we all have an Internet nerd tendency to fixate on a couple of axioms and derive the rest of the world from them, rather than reading the huge legal documents that set these things out
Moreover, the issue brought their business model into public spotlight, and people realized the problems with making money by selling order flows and the conflicts of interest that came with it.