That's a reason, but I suspect not the prime reason. The ACLU, the Institute for Justice, Pacific Legal Foundation, etc. usually never have a direct claim them

That's a reason, but I suspect not the prime reason. The ACLU, the Institute for Justice, Pacific Legal Foundation, etc. usually never have a direct claim themselves in the cases they're involved in... they look for some other party that has standing and then assists that party in pursuing their case in court. I don't see why the FSF could not also follow that model by supporting any copyright holder in litigating/negotiating GPL license breaches. What they do get with assignment is that they can ensure that the software is only ever issued under the license/license version of their choosing. Any other copyright holder can cease distributing their software under the GPL; true, they cannot revoke previously granted rights, but future versions, etc. can be made to be non-FOSS. An independent copyright holder could also dual license their code GPL and closed source. I think avoiding those scenarios is really why FSF wants the assignment. Not the ability to litigate, that's just an excuse.