If we have well designed autonomous AI vehicles, then why won't the USA government allow it to be witnessed in the public?
The question is based on a false fact: in Michigan, it is currently legal (under certain conditions described here ) for an autonomous car to operate without a driver.
The reason that the federal government has not enacted any direct legislation (although they have enacted guidelines) on autonomous cars is because it is still a developing technology (as great as those Cruise videos look, I wouldn't trust most companies working on the technology to have driverless cars on the road without operators) and that it arguably falls under the state governments jurisdictions. Some companies have appealed to the House to pass national legislation to allow autonomous testing (GM, Toyota, Lyft), but nothing has come of it yet.
This answer addresses the incorrect assumption that the US government prohibits it (that is, here's no federal law against it, but state laws vary), so I will address the incorrect assumption that there now exists "well-designed AI".
If you look at the actual reports submitted by the autonomous car companies who have tested in California, you'll see that most can't go more than a couple of hours of driving without an unexpected need for operator intervention. Waymo's (Google's autonomous car spinoff) system is more reliable as far as unexpected interventions, but their report emphasizes that routine operator interventions happen many times a day. Autonomous vehicles that can operate without a driver in any but the most controlled circumstances are still years away.