Well, it's more about what happens if something bad happens to the FSF? What if they get acquired and then $BigCo gets all of the copyright assignments. I don't believe that the FSF would betray people like that, but there may be situations where they don't have a choice.
This is an unlikely scenario. The FSF is a 501(c)(3) charity, which means they have to work for the benefit of the general public and not to give an advantage to any particular person or for-profit company. If they would ever do the latter, the following IRS audit would not be fun.
Many proponents of copyright assignment to for-profit corporations have argued that "it's just the same thing as what the FSF does, so it's fine", but their legal nonprofit status makes it a substantial difference.
A better argument against the FSF's copyright assignment practice is that it is bureaucratic overhead for somewhat questionable benefit.
I've actually discovered since that the FSF's CLA actually explicitly states that you give them your copyright under the condition that they always provide it under a copyleft license. So it looks like I was wrong about that and might even start contributing to GNU projects.