No.

The hardware attestation (which is used by strict Play Integrity) checks the signature on your OS. It is totally possible to allow signatures other than Google, but Play Integrity doesn't do that.

Companies could totally decide to use hardware attestation and accept systems signed not only by Google, but also other systems (like GrapheneOS). But they don't care because not enough users complain to them.

Users of alternative Androids typically silently move to another service or stop using it entirely. Which is understandable but doesn't help the cause.