Google could do this now across their suite of apps by using iOS's keychain APIs.
Apple has technical limitations in place to prevent alternatives from being as good as the default. A simple example is setting the default browser/email application. I'm not sure if this is still true, but Apple had a policy preventing 3rd party browsers from being anything more than a skin over Safari.
Since Apple is in complete control of the App Store and there aren't any 3rd party app stores, Apple has no incentive to allow alternatives to it's default applications.