GrapheneOS points out how its improved privacy and security should mean that it is accepted in a system like play integrity. But this is just to outline how flawed the logic of play integrity is. It is by no means an endorsement of play integrity. GrapheneOS wants people to know that google is lying and breaking the law, and uses its own exclusion as that evidence. Even if GrapheneOS were accepted into play integrity, it would still exclude any and all forks and self-signed builds of GOS, which is unacceptable. If companies absolutely insist on using this approach despite its flaws, they should use the generic attestation available in android, and permit using 3rd party roots of trust in some form, rather than outsourcing this verification to 3rd parties like google.

As for the pinned attestation approach, that is Trust On First Use, and is used to verify the integrity of a device based on the security of the devices early bootchain. The initial attestation is what future attestation is pinned to. This allows you to verify a device is the same one, it has not been downgraded, has not been tampered with, etc. This is awesome, and lets you do things like what GrapheneOS does with Auditor. But this is not used to restrict what operating systems are used. Root based attestation somewhat tries to resolve the Trust On First Use approach, but is used to arbitrarily ban operating systems in practice. It is super flimsy as any leaked keys can bypass it.

My only concern is your claim that GrapheneOS is for this technology when it is most certainly against it. The nuance is that pinned attestation is a different approach with different properties, and advocating for it does not mean GrapheneOS is not an ally against play integrity.

Auditor also functions as a proof of concept for the potential of attestation, check here for more info: https://attestation.app/about