Here is a copy of my other comment in the thread, which I think is relevant to your post too:

I thought the latest lawsuit from Software Freedom Conservancy was interesting, they are suing as a third-party beneficiary of the GPL (not as a copyright holder, although they probably could do that too in this case) and seeking specific performance of the GPL violator (Vizio) and of course legal costs, but no damages. The specific performance they want is of course GPL compliance. As part of the case, they are basically saying that the GPL is a contract and the contract says that third-parties can get benefits and so they want those benefits. Frankly this is a brilliant case and if they win the precedent will allow anyone to sue over GPL violation. If any trolls try it, all they get is GPL compliance, so they have no incentive to try it.

https://sfconservancy.org/copyleft-compliance/vizio.html

Couldn't the FSF sue on their behalf?

On what grounds? The FSF has no standing to sue like that. The software freedom conservancy has lawyers who will work on copyleft infringement cases like this but a copyright holder still has to step forward as a plaintiff.

They could just provide legal support without being the plaintiff. They have done so before (or rather the Software Freedom Conservancy (Conservancy)):

>That is how the FSF and Conservancy have always handled compliance. The FSF has done compliance work for the GNU Project for decades, and in all that time, we have only been forced to file a lawsuit once. The suit came about after years of working with the violator trying to correct their compliance. Even in that instance, where the FSF eventually did have to sue, the violator later went on to become a contributor to the GNU Project, and continued other free software activities as well. Conservancy has a similar track record of avoiding lawsuits; they are currently funding Christoph Hellwig's lawsuit against VMware in Germany, which marks the first time Conservancy has ever been involved with a lawsuit regarding Linux, and their FAQ explains the lawsuit came after four years of friendly efforts by many parties asking VMware to follow the GPL's requirements.

https://www.fsf.org/bulletin/2016/fall/the-role-of-lawsuits-...

>Conservancy maintains this FAQ list regarding Christoph Hellwig's lawsuit against VMware in Germany over alleged GPL violations on Linux as a service to the Free Software community, and in particular, the copyleft community. Conservancy realizes this lawsuit generates many questions and interest from the community. Legal counsel (both Conservancy's own, and Christoph's lawyer, Till Jaeger) correctly advise us to limit our public comments regarding specific details of the case while litigation remains pending in court.

https://sfconservancy.org/copyleft-compliance/vmware-lawsuit...

The copyright holders can delegate the ability to sue to others, so FSF could do that if delegated. Software Freedom Conservancy have a similar delegation and copyright aggregation programs for Linux and Debian developers:

https://sfconservancy.org/copyleft-compliance/

No, only the copyright holder. If it were an FSF program where they owned the copyright then they would (this is one of the reasons the FSF requires copyright assignment).