For the record I don't think the FSF asks that all GPL software gets assigned to them. However for all GNU software (bash, gcc etc) They want copyright assignment.
My bad. I knew that they didn't really ask for assignment to them for all GPL software, but I was under the impression that at some point, at least, they were suggesting something along the lines of "if you want our legal representation then feel free to assign the copyright to us". Not in a mafia 'protection' way, either, but more of a logistics thing than anything.
Either way, that doesn't seem to be the case.
I can completely understand why they want copyright assignment with the GNU software, though. Having everyone keep their copyright 'feels' nice, but how many projects have we seen that end up almost frozen because they want to do something with the license but can't find all of the copyright owners, let alone get them to agree?