Inspired by this thread, I tried back-in auto-park today at the local Office Depot. Between a low slung Ferrari and rather tall Rolls Royce, (actually a Prius and a non-de-script SUV), the back-up was smooth and uneventful. After pulling in, the car realized that it wasn't very well centered and so it did a little forward-backward wiggle to get centered.
I didn't like that the chipped old driver-side Prius door was close to mine, so I adjusted the car a little farther from the Prius. Maybe a little more parking A.I. could take care of this.
BTW, a similar issue in parallel parking. Rather than centering between two cars, if I can't get a front spot, I like to move the car slightly rearward. Drivers (especially without back-up cameras) can judge the distance to my rear bumper more accurately then my front. (This was especially true on my '87 Corvette).
Here's something to think about:
Auto-parking is fine for parking. But what about un-parking? Have you ever been squeezed between two cars with minimal space to wiggle out? Power steering and the tap-tap sound of bumpers helps wiggle out.
But what if the car could do this? Getting to within a fraction of an inch to each car while going maneuvering out while checking for traffic could be a pretty cool feature; especially for those who live in high density areas.