I think there's a misunderstanding here on what "use" means.
> You could ignore the GPL and static-link a piece of software to a GPLed library, but if you did so, you'd legally need a different right to use the GPLed library, because you hadn't complied with its license terms and so only have your minimal rights to use someone else's intellectual property.
Before we get into anything particular to the GPL, Galoob v. Nintendo established that modifying copyrighted programs for personal use is covered under fair use [1], so you could use, i.e. run, that newly linked program without any regard to license.
Even if the GPL could establish such restrictions, I don't think that it would. That seems to run entirely opposite to the spirit of the license. The point of the GPL is to preserve the freedoms of the end user, and freedom 0 is to freedom to run the program [2]. When you link that program and run it, you are the user. The author of the GPL work wants you to be able to run the GPL code "as you wish, for any purpose", and they also want the same freedom to be given to whomever you give that code to. If you give that linked program to someone else, they're the user, you're the distributor. Your freedoms as a user are the same as they've always been, and that user that you gave the code to needs those same freedoms.
> Said differently, the GPL doesn't try to apply itself to "derived works" because of some contralegal dictum they don't have a different creative origin. It merely says "you have two choices - license the things you link with OUR stuff under OUR terms, or you don't have the right to use our stuff".
You have the right to use the stuff by virtue of freedom 0, literally "the freedom to run the program as you wish, for any purpose". You don't have the right to license "OUR" stuff to other people without also ensuring they have the same freedoms that "we" gave you.
See also another commenter discussing freedom vs. power [3].
[1] https://en.wikipedia.org/wiki/Lewis_Galoob_Toys,_Inc._v._Nin....
[2] https://www.gnu.org/philosophy/free-sw.en.html
[3] https://www.gnu.org/philosophy/freedom-or-power.html
EDIT: formatting