The FSF does give that exact permission in the GNU GPL FAQ, though in the same breath they urge you not to use such permission, which would contribute to the already-overwhelming problem of license proliferation:
Can I modify the GPL and make a modified license?
It is possible to make modified versions of the GPL, but it tends to have practical consequences.
You can legally use the GPL terms (possibly modified) in another license provided that you call your license by another name and do not include the GPL preamble, and provided you modify the instructions-for-use at the end enough to make it clearly different in wording and not mention GNU (though the actual procedure you describe may be similar).
If you want to use our preamble in a modified license, please write to for permission. For this purpose we would want to check the actual license requirements to see if we approve of them.
Although we will not raise legal objections to your making a modified license in this way, we hope you will think twice and not do it. Such a modified license is almost certainly incompatible with the GNU GPL, and that incompatibility blocks useful combinations of modules. The mere proliferation of different free software licenses is a burden in and of itself.
Rather than modifying the GPL, please use the exception mechanism offered by GPL version 3.
As you can see, they permit reusing and modifying the terms of the license as long as you change the name and remove any association with the GNU project.
I suppose the reason that this right is not offered within the license text itself is so that the FSF can rescind or modify the terms of this permission in the future. That is, if the FSF decides to change how or whether they offer the right to make modified forms of the GPL, they do not want to have to issue a new version of the GPL just for that change! (Similarly, if they wanted to make the permission more restrictive, there would be no legal mechanism to say, "Sorry everyone, that part of the license is wrong; we retroactively eliminate the version of the GPL that allowed you to make changes from existence.") Therefore, the license itself offers no rights to make a modified version, and any such rights are offered via an external channel, such as the GPL FAQ.