Putting on my "personal opinion" hat;
If a platform gave users this option per credential, and there was any visibility to that choice on the relying party side, the replying party would likely just reject the credentials they don't like outright, and tell people 'go figure out how to twiddle this setting if you want to use your phone here'.
Part of the web focus of these APIs mean that they will default to being open and user centric - features that might enable relying parties to block user choice will receive tremendous scrutiny, and proceed very slowly. Sites are expected for now to accept what the user chooses, and do additional steps as necessary to meet their needs. This means passkeys as a whole are not going to be always accepted as a MFA replacement.
Even features like hardware attestation are gated by a prompt by some browsers, because some consumer-facing websites went live with code saying "we will only support this one brand of security key". This led to some of the warnings in the document here: https://www.chromium.org/security-keys/
I can sympathize with the desire of a "footgun mode", which might even lie to the website about whether the credentials are backed up. However, I wouldn't trust something that critical to what is almost going to be a poorly maintained path through the system. Instead, I use (two) Yubikeys for such credentials.