At some point the word will go out that it’s over—“we won”—and everyone will rush to sell their GME and take profits.
It’s not possible for all those people to succeed. Broker apps like Robinhood will be absolutely overwhelmed with sell orders, many of which will run into technical problems and/or no counter parties. A lot of people are going to be pissed off and blame the brokers.
People buying in late will have the most to lose and maybe the least understanding of what is going on. I mean, this story was a “breaking news” red banner on WashingtonPost.com yesterday. Not everyone buying GME today understands the social movement /r/wsb angle.
Ultimately brokers are worried about getting sued by people or companies who lose a lot of money in ways that will look preventable in hindsight.
Edit to add: the 2008 financial crisis was caused by financial firms selling a lot of crazy mortgages to people who could not afford them unless housing prices went up forever. When the crisis hit, the firms got the blame, not their customers. Companies learned that helping their customers shoot themselves in the foot can come back to bite them, even if it was all legal and what customers wanted at the time.