Post scarcity could mean many different things. One alternative to scarcity is consent. Behave in a way where enough people revoke consent, and your money won't go far enough to buy anything. So in that model they'll share access because if they don't they lose.
Control over AI ? What money ? Money is just a tool to facilitate cooperation. If you have superhuman AGI you don't need anyone else to do things - they are just a threat for your control - so you eliminate that threat either by destroying or neutralizing any viable threat scenario (harmless pet).
Not sure why a superhuman AGI would take orders from a human, but ignoring that for a moment...
Intelligence is not the only bottleneck on getting things done. Yes, eventually it could build its own robot minions and farm food for its master and construct some kind of army of hunter killer bots to ensure compliance and dominate the planet, but that kind of conquest takes decades, if not centuries. Maybe it can play 4 dimensional chess, but we still have some advantages.
We need post-scarcity economic models so that we can ensure that cooperation > individual continues to hold. The scarcity-driven ones we're using currently don't give us any legal nonviolent ways to stop outcomes like this, but that's not a law of physics, that's just a quirk of history.
I think there are a million more immediate risks than a robot uprising, but as it turns out, putting a steering wheel on our economy would help with those too.
Why would anyone share access ? It's a one shot prisoner dilemma - whoever controls the best system first eliminates the competition and wins.