This issue comes up every few months or so, and the main answer is the same.
The reason the current Auto Train works is because there is a massive market for NE to Florida travel, and they all travel along the same corridor (I-95). If you are driving from New York to Florida, you're pretty much driving right past both auto train terminals. The route is short enough that it can be done with a quick overnight, allowing people to sleep half the time the train is moving, and wake up, eat, and get off the train. You can start out pretty much anywhere in the Northeast in the morning, and make it to Lorton in time to catch the train (while not driving out of the way), and upon arrival at the other end, get to wherever in Florida you were driving by the end of the day. Same thing on the reverse trip.
There really isn't any other corridor that meets the same conditions.
People mention midwest-southwest as a possibility, but where would you put the terminal that would be on the way/in the right direction for people heading there? It can't be Chicago because Chicago alone won't support a route like that (the population is too low vs. the population of the DC-NY-BOS corridor, which is the main catchment area for the Auto Train). Chicago is too far north for folks in southern Illinois, southern Indiana and Central Ohio, and too far east for folks in western Wisconsin, Minnesota, Iowa, etc.
It could be a place like St. Louis or Kansas City, but then you're stretching the range of how far people have to drive to get to the train from places east of Chicago or in northern Wisconsin.
The NEC-Florida market is also more massive because Florida is more than just a place retired folks go in the winter. It also has year-round attractions for families, which make up a decent portion of Auto Train's ridership. Arizona really doesn't have any attractions. It is true that Southern California does, but now you're turning it into a much longer trip (a minimum two-night trip), which causes the market for land-based transportation to drop off quite a bit vs. a quick overnight.
Long story short, IMO the population of the Midwest is too spread out and the distances too long to make an Auto Train really successful out that way.