It's not just merely to bring a law suit. Each author of a joint work has an independent right to grant nonexclusive licenses. So if you and I were joint owners of project Foo, I could grant a nonexclusive license to Microsoft to use the entire work even if it was your intention that our work only be licensed under the GPL. You could sue me, but not Microsoft (and Microsoft might even be able to indemnify me).
This is why the FSF wants all the copyrights. When they bring a suit they don't want damages, they want an injunction. But all the company being sued needs to do is pay some random joint author for a nonexclusive license and then the company is effectively off the hook as long as they can absorb any monetary damages. That joint author must account for payment received by sharing with all the other joint authors, but that hardly changes the equation.
Also, things get very muddy when you're talking what constitutes a joint work, versus a collective work, versus an insubstantial contribution. If you're the FSF that makes negotiating with an infringer more difficult. It you want the threat of litigation to be taken serious, you need to get rid of all of those sources of doubt and confusion.
But note that most people cannot actually transfer all of their interest to the FSF or anyone else. An author of a work not done as a work for hire (as with much Free Software) has an inalienable termination right. (See S.203 of the Copyright Act.) 35 years after the original transfer or license an author can unilaterally terminate those rights. Counting from 1985, that means that by 2020 it's possible (though I suppose very unlikely) that some people would rescind their grants to the FSF.
In fact, it's theoretically possible for someone to even rescind their GPL licenses! This is why lawyers say that it's impossible to put something into the public domain--if you die your successors can exercise that termination right. But there are lots of technical issues--like notice--with terminating license to an indeterminate number of people.