They do, and I believe it's because it gives them a better platform from which to pursue GPL violation claims. I think that's basically sensible and an exception to OP's general statement -- if you're contributing to an FSF project, you need to understand that what you're doing is political as well as technical. You're giving FSF more ammunition with which to enforce copyleft. FSF is an exception to the concern that the asignee of your copyright is going to do a proprietary relicensing.
In other words, "do as I say, not as I do".
That's an odd conclusion to draw from my post. Are you under the impression that OP represents the FSF? He does not. Neither do I. My point is that the general rule that one should be wary of CLAs because they can be used to take away your software freedoms probably doesn't apply to the FSF. A different consideration applies to the FSF -- if you don't like their political goals, don't support them by contributing to their projects.
Anyone can assign their copyrights to the FSF. So no. ;-)
It figures - the FSF are believers in releasing under "GPLv3 or later", which almost no-one does, as the FSF are of course empowered to do whatever they want with future GPL versions.