> Doesn't the AGPL specifically disallow that?

It can disallow downstream licensees from doing things with it, it can't prevent the copyright holder and licensor.

> If I understand correctly, the FSF has even directly threatened legal action against developers who add extra restrictions to the AGPL. The license text is copyrighted, does not allow modifications, and includes terms allowing the user to ignore any additional restrictions, so adding extra restrictions would seem to either be ineffective or a copyright violation.

If it's a copyright violation of a copyright on the license, that has no effect on the effect of the license between the licensor and licensee, though it may result in money being owed by the licensor to the copyright holder on the license.

OTOH, I think any US court would find that a party trying to control the legal effect of licensing arrangements between third parties by leveraging a copyright on license text is, itself, a fairly strong indication that the particular use of the license text at issue is outside of the scope of copyright protection. That's not protecting expression, it is instead creating a roadblock to the freedom of contract.