If allegations in the report are false, the traders face legal liability. If they’re true but the market disagrees with the impact, they’ll lose money on the trades.

What specific thing should the SEC be policing here?

Also, if markets don't move following such a report short sellers stand loosing a ton of money, even if they are right.

Among other companies brought down, rightly so, is Wirecard. And they played the "mean, evil short sellers try to manipulate the share price"-card hard. So, shoet sellers do have a place in our modern financial system.