You’re welcome to want service operators to do that, but not doing it doesn’t affect any of your software freedoms.
The later half -- the freedom to change the program -- is meaningless in a world of attestation. Tivoization was explicitly forbidden on these grounds: if you can modify the software, but cannot use it in its modified state, the distributor is in violation of the spirit of free software and in particular, GPLv3.
It is a basic argument from positive liberty: the freedom for services to discriminate based on user's software and the freedom of the user to be discriminated against is no freedom at all.
Free software does not mandate service operators to interoperate between their own infrastructure and custom or modified software you possess. You are not somehow guaranteed access to someone else’s system just because your local code has a FOSS license.
The latter is what I mean. Web Integrity or SafetyNet are a closer counterpart to this situation than your curl example. A user agent is just a hint; attestation is an effective enforcement mechanism.
No Free Software license on my client can obligate your server to cooperate. But if attestation becomes the norm across many different services, the entire framework of user choice Free Software stands on collapses.
How would Ungoogled Chromium survive if every second website rejected non-Google Chrome? We've already seen this play out with Android: more people daily-drive GrapheneOS than Lineage because it passes Google's lower-level integrity checks.
And when a "strongly advised" government app requires the strictest attestation level, will you have to move countries just to exercise that freedom of choice you supposedly have?
In the same way that commercial entities aren't guaranteed a business model just because they want one, free software isn't guaranteed connectivity to other people's systems just because otherwise it's less useful.