I hear you. It really depends on your requirements. That said, any site that is currently enabling 'google login' or 'xyz login' other than just a standard email login is already doing this. Never mind the fact that significant numbers of users are already on gmail or google apps.

The trade-off being that you can run the risk of a security hole in your authentication flow.

I still miss Mozilla Persona.

I also looked up the terms... this is the only thing I noticed that was relevant... 'except as necessary' is pretty vague, but I'd take that to mean that they should probably inform you first.

https://cloud.google.com/terms/

5.2 Use of Customer Data. Google will not access or use Customer Data, except as necessary to provide the Services and TSS to Customer.