1. The problem with RobinHood's behaviour here, is that they are doing price manipulation (By only allowing sells, instead of buys.)
2. Price manipulation isn't really a crime against their customers, it's a crime against the stock market. Their customers will sue them, but probably won't get much. It's a bit hard to make a case for "You stopped me from trading, when I was planning on making a lot of money from trading, by cashing out right before a bubble popped."
3. The SEC is supposed to deal with crimes against the stock market. They may or may not sanction RobinHood, but I doubt the sanctions will be serious.
4. The SEC might look into the obvious collusion problems, where the owners of the GME shorts may have reached out to the exchanges/settlement networks, and tried to block retail traders from buying GME. This may or many not result in financial penalties. Even if sanctioned, this may be worth it for the owners of those shorts, because the alternative is bankruptcy, complete financial ruin, and the sale of their children, their grandchildren, and their great grandchildren into sixty years of bondage.
5. Your thesis is sound, but the SEC works with, and for large players in the market. Those players want a mostly-fair market. If the counterparty on the other end of these trades were not retail morons on reddit, the SEC might be a bit more heavy-handed in their enforcement. The thing is, most price rallies are not driven by retail morons on reddit... So, if your business plan consists of "Short a stock to 100%, then call up all the exchanges and settlement networks, and tell them to only allow you to buy stocks," there's going to be a lot of really wealthy counterparties to your trades, who are going to be really, really pissed, and you will probably lose all your money and go to jail.
#5 is unlikely to happen here, because the narrative around this is 'Ha, look at all the dumb retail money driving a bubble, we are just deflating it before retail traders get burnt.' And that narrative is partially true, which is why it's making the news cycles, and serious talking heads on the television repeat it with a straight face.
... Also, I would like to point out that there is nothing wrong with shorting a stock, or shorting a stock past 100%. Yes, it can trigger a short squeeze. No, I don't really think there should be rules against it, or against short squeezes. These are institutional investors, who surely must understand that short-selling a stock carries unbounded risk. If they wanted bounded risk, they should have bought puts.