A significant part of that 'computer science problem' is data collection (including training the AI with that data) . By putting the hardware on the car, Tesla is getting many orders of magnitude more data.
Yes, Tesla's approach is to get something out there that works at least part of the time, then collect data from all the cars and process. In a few months Tesla cars with AP had driven more miles and provided more data than Google had collected in a few years of testing.
I read a year or so back one thing that has been holding the mainstream car makers back in making EVs is they are afraid to commit to one technology only to have a major new chemistry come out and require they retool for the new chemistry or end up falling behind the curve to competitors that waited and adopted the better chemistry first.
In this respect car companies tend to want to be way behind the cutting edge of new technology. They trade reliability for newness and are somewhat risk averse.
Tesla has tech upgrade built into their model. The mass produced cars probably won't have the constant change the S and X have had, but they probably will do upgrades to the cars once or twice a year. As far as AP hardware goes, when Tesla parted ways with MobileEye, I think that just hastened the introduction of the AP2 hardware. AP2 did come out shortly after the falling out. They figure that when AP hardware gets better, they will just incorporate it into the cars.
All these changes do have their downsides. For one thing it makes the spare parts situation for their cars much more complex than for mainstream cars. Getting parts for a 2015 Model S can be tough. The part you want may have only been in the car from say April to August with cars made before and after that date using a different part. Tesla is also notoriously slow at producing spare parts too, so cars damaged in accidents can sit for months waiting for spare parts. This is something Tesla should address by setting up a separate spare parts line to make spares for all their older cars. Parts that have some demand like body panels should be made in advance and stored and low demand parts should able to be turned out quickly as needed.
But again, constantly improving the cars means they need to support a much wider catalog of parts. That's one of the reasons car makers only make changes to their cars once a year unless there is some sort of safety recall or something.
Tesla's model is a Silicon Valley model. Evolution of electronics has slowed as the IC market has reached the edge of Moore's Law, but for the last 40+ years, tech companies had to deal with the hardware and software evolving significantly on a year to year basis and they had to adapt or die. Cars have evolved much more slowly and car makers are used to a much slower rate of change.
But making changes to a complex mechanical machine is different from the computer industry. The jury is still out on whether Tesla's Silicon Valley approach to cars will work when there are millions on the road. Some ideas don't scale well.