Isn't the best way to verify the integrity to use git signed commits? GitHub has great support for this

You’re mixing up integrity and authenticity: git provides integrity through its basic design; commit signing additionally adds authenticity (sort of).

But again: you don’t actually get authenticity if you obtain the public key from the same untrusted channel as the signed material. The key has to come from another channel (another simplification, but true in PGP and git’s case). That channel can be the user’s GitHub profile, website, etc., but it can’t be the repository itself.

Fun fact, just as SSH public keys for a user are readily publicly available on GitHub, gpg keys are as well

    curl https://github.com/${username}.keys
    curl https://github.com/${username}.gpg | gpg --list-packets

Interestingly enough, since changing the GH keys is subject to GH authentication (possibly involving 2FA), the owner's key is kind of validated (by GH) so it _kind of_ makes GH a gpg key notary.

Having `git log --show-signatures` validate _all_ signatures is then a matter of:

    curl https://github.com/${username}.gpg | gpg --import

Now I kind of wish GH would sign such user pub keys _at the time they're added_ (thus at the time GH authentication is deemed valid), thus ensuring they've not been tampered with in between.

With a bit of UI GH could present a UI for a user to validate another user's key, and sign that assertion (with a GH private key, not the user's of course) as well.

Of course it hinges on trusting GH, but GH already signs e.g UI borne merge commits on your behalf so there's that.

Then next step would be for GH to host an actual key server to accept off-band signed keys containing a magic comment that bind the keys and sigs to GH usernames...