The provider might notice that their key is being used in an unauthorized way and terminate your account, prosecute you for computer fraud and abuse, etc.
I think this is the only assured way to interop, as I expect Google may try to kill other competing apps (specially in mobile) that does not capture user data or generate data points for its ads.
I wonder if any intentional limitation here should not trigger some of the EU Digital Services Act provisions for interoperability ... in this list [1] I see Google Play, Maps, and Shopping but not GMail!