Best case scenario for ASI is that they create enormous wealth and will keep humans around as pets because it costs essentially nothing, like in the Culture series by Ian Banks or The Polity series Neal Asher.

Humans are extremely costly in terms of the resources we need in order to survive, the space we take up, and the messes we make (everything from the shit and piss we generate to the wars/destruction/death/violence we inflict on pretty much everything around us). We'd make for entertaining pets, but we're the farthest thing from low maintenance. Even ignoring that all other animals on earth share many of the problems we'd impose on our owners we stand alone in having done devastating amounts of damage (some irreversible) to ourselves and our planet.

I'd hope that they'd keep a few of us around, but it's hard to see the logic in them keeping all of us and allowing us the freedom to live and breed the way we do right now.