I'm not sure what you're trying to say exactly, but I'm pretty sure that this already exist and there are multiple solutions and self-hosted registries as well for it. Check out Harbor:
I'm not talking about private hosting of containers, I'm talking about an alternative to today's public registry of container images that is 100% verifiable so that when something like this happens it is possible to be certain that no one has tampered with any of the container images.
Do you mean formal verification? Verifying such a vast web service may be nearly impossible, especially since you'd still have to rely on a database server, os, and kernel, the most popular of which are seemingly fundamentally incompatible with verification.
You can only have 100% verifiable container images if the Dockerfiles uploaded by users are reproducible (in the sense of https://reproducible-builds.org/). The vast majority probably aren't, and I'm not sure the Hub could reliably detect those that are.