Earlier quoted context omitted.
The FSF is not 'attacking' such licenses, they're just arguing that they aren't free libre software licenses. It's the SSPL people and others, by trying to co-opt the free and Libre software movement by claim their licenses are something they are not, which are mounting the assault. And let's be clear it is a pernicious, aggressive and deliberate attack threatening, and in some cases knowingly intended to fundamental…
And the FSF has even come up with their own license for network services, namely the AGPL - that is a full free-software license, since compared to the GPL it only clarifies requirements around public performance of the covered work (which unlike mere "use" of the software, is something that copyright law expressly grants as an exclusive right of the copyright holder!)
Most people never get that far, because they write the license off as an attack on principles. The debate about the substance didn’t really get to happen.
As for public performance, I’m not aware of any case law to suggest that the public performance right applies to software as you suggest. And I’ve never seen FSF or independent legal counsel argue that GPLv3 and AGPLv3 are functionally equivalent due to background law.
The FSF theorists I’ve read describe AGPL as “synthesizing” a public performance right for software that doesn’t otherwise exist under current copyright law. They do so out of two existing exclusive rights: the right to prepare derivative works (making changes or building larger programs) and the right to reproduce in copies (incidental to use).