Defining what is a "reasonable government request" is a valid question, but it's really just not that high of a bar to get a records subpoena/search warrant for video like this. Courts sign off on those routinely, so I don't think you can really expect Ring or any company that holds your records to deny police requests for very long.
The system they have seems pretty balanced. The police look at the ring website to see who has cameras (they could figure that out by walking the neighborhood), they ask for the footage (instead of knocking on the door), they get turned down (or not), they get a warrant, the footage is released. Ring is reducing the overhead of asking somewhat, but they're not enabling mass surveillance or building AI systems that track suspicious people across multiple ring devices.
Is there something I'm missing here? If you record video of your front yard, and the police want to see it, they have a right to, subject to the normal judicial review.