They have enforcement powers if they they prevail in the suit and the people who have legal power enforce their will. Which is something that has happened in the past. That includes them just successfully abusing the defendant into settling, no matter if they would have won in the long run.

The RIAA clearly has the power to enforce economic harm on anyone who has to defend their lawsuits. Against small enough defendants, that makes their positions extremely relevant.

The basis of copyright in the US is that being able to sue and win is an enforcement power.

That’s the core thing the government is giving copyright holders, and what the public is protected from when something enters the public domain.