That key will leak eventually, it's too juicy a target.
You describe chat control as if it's just an AI csam scanner that runs locally on your phone, like what apple did recently-ish.
Chat control is so much more than that, and so much worse
That's not my understanding. My understanding is that ChatControl will run client-side scanning and report what is deemed illegal.
This is not a master key to all communications.
On the contrary, it is an argument in favour of extending ChatControl to using machine learning for detecting such cases.
The problem, again, is that we don't want to have an opaque system that can be extended to surveilling new things, because it's very difficult to audit and make sure it is not abused.