alt Hacker NewsFreedom 0 is not violated. GPL includes restrictions for how you can use the software, yet it's still open source.
You can do whatever you want with the software, BUT you must do a few things. For GPL it's keeping the license, distributing the source, etc. Why can't we have a different license with the same kind of restrictions, but also "Models trained on this licensed work must be open source".
Edit: Plus the license would not be "GPL+restriction" but a new license altogether, which includes the requirements for models to be open.
That is not really correct, the GNU GPL doesn't have any terms whatsoever on how you can use, or modify the program to do things. You're free to make a GNU GPL program do anything (i.e., use).
I suggest a careful reading of the GNU GPL, or the definition of Free Software, where this is carefully explained.