I worked in proprietary trading for about half a decade.
I think the biggest thing that the lay-person doesn't understand is that thinking of hedge funds (and other proprietary firms), banks, exchanges and ATS's, retail brokerages, the SEC, and lawmakers as all being either one entity or all being on the same side is just absolutely incorrect. They all need each other, but by and large they are not friends.
Some claims I've seen that are just comical to me:
"The SEC is going to step in to save hedge funds"
The relationship between regulators and proprietary firms is particularly cagey. The SEC constantly audits them and asks, in my ex-professional opinions, extremely annoying questions about even the most innocuous trading activity. (Annoying because they take so much time because frequently, not knowing what the firm is doing, they ask questions that internal tooling is just not prepared to answer, thus requiring custom development; and annoying because some of them feel like they're just the SEC trying to use their authority to conduct audits to learn more about the industry). But I digress. The SEC is absolutely not going to step in and do a prop shop a favor. Their concern is with the efficient and accurate functioning of the equities market. The fact the GME, a company with no news releases and no change in their (honestly dismal) fundamentals, has experienced such absolutely insane volatility (there are large numbers of options contracts with less volatility, for crying out loud!) is absolutely a concern for them. The fact that "what is the price of GME right now", asked to a person who looked at Apple Stocks app yesterday but not yet today, is "somewhere between 10 dollars and 1000 dollars", is absolutely a major cause for concern to them. Equity markets exist to discover pricing and transfer risk. It's hard to transfer risk if you don't have any idea of the pricing!
"retail brokerages are cancel culturing the GME rocketship!" and similar rhetoric, especially with aphorisms suggesting that the SEC or shadowy "the rich and powerful" are pressing them to do so.
I really, really doubt it. Retail brokerages toe a very fine line, because on one hand they obviously really want people to store their money with them (e.g. Schwab makes like 80% of its operating revenue from interest on uninvested cash balances) and also to use their trading services. But at the same time, they are taking as clients some of the most dangerous creatures known to man: retail investors. They're dangerous because they have so little clue what they're doing (which is like, fine, you know? this is no judgement on them) that there is a very real responsibility places on the retail brokerage to protect them from themselves. There's a reason you have to apply and be approved to trade options, and there's various levels of approval for various risk categories too. You need at least 25k in balances to be a pattern day trader. There's precedent for brokerages limiting access to some ETFs that expose equities investors to the kinds of leveraged risk that is more typical of options. Brokerages have been sued - successfully - for not doing their fiduciary duty to educate investors about risk.
I am absolutely unsurprised that retail brokerages are limiting trading of GME, AMC, etc. I can already see the lawsuits coming when this thing folds - "Why did you let me trade GME given the volatility, especially after the SEC even made a statement about it? I am a retail investor and your client, and cannot be expected to know better, and you failed in your fiduciary duty to me." This is absolutely something a retail brokerage would do to protect themselves from regulatory scrutiny.
(I had more to vent, but this post is already huge so I'll stop here. You get my gist, though.)