1. That sounds like an Anthropic concern, not a concern for most customers who don't run their own model.
2. This still requires trust in the provider, I imagine these proofs would change weekly as they tweak their models, and you have zero knowledge of what the changes are, you just know you're getting version 11.12.1999 - does that really help you if the provider is maliciously downgrading after release? All you know is you got the same version as everyone else, not what that version is.
3. Again, if you don't trust the provider, it's game over - you're sending them all of your data. Knowing a version number is not going to help you much.
I'm not convinced this is useful for problems most people face using models, it seems a very niche academic concern frankly and an incredibly complex system to prove not very much.