I know you meant more than this, but I'm sure automating opening and closing the doors will be a lesser challenge then developing autonomous self driving?
There is a certain romance around good service, but the good service is not the reason why people use taxis here.
One could make a similar argument that self service restaurants serving revolving sushi, or tablet ordered sushi miss the good service of a great restaurant. Yet these places are wildly popular, because one goes there to eat.
Toyota JPN Taxi[1] replaced most sedan cabs, and it has electric sliding doors which is nicer than swing-out doors. Already opens and closes with electronic commands from driver seat. No big deal.
Searching, I see references to automatic doors preventing robberies but no explanations as to how that would be. Perhaps the barriers between the back seat passengers and driver prevent knife threats? I wouldn't expect robbers in Japan to have guns, like they would in the US.
Oh, maybe you mean the automatic doors are "waiting for you with the open door"? A lot of cars have hatchbacks that close using a remote, either on the dash or on a fob. It was big news that people were demonstrating the CyberTruck cutting carrots or hot dogs because people are used to hatchbacks closing and opening safely. It seems a lot simpler to automate doors opening and closing safely than autonomously driving in Tokyo.
But true, even Uber is kinda flash with driver wearing white gloves.
Most taxis in Japan have driver-controlled doors. The driver doesn't have to get off the seat at all. Given it is already automated, it is trivial for a driverless car to do.
A taxi we called up using Uber (Uber can only call taxis in Japan) even delayed cancelling our ride passive-aggressively long enough that we missed other rides and lost a lot of time.
My friends had even met with a rude taxi driver (I know impossible, in Japan, right?) that refused to take them to a place that he deemed too close in Kyoto.
We also had numerous great experiences with taxis too: accomodating our stops, having lovely conversations, giving out touristic information and they tried really hard to go accross the language barrier. Great people overall. But, having said that, as a tourist, I'd take a Waymo any day over a taxi in Japan just because I think it would be less friction for me.