Well, that’s Waymo (in Phoenix) which has put out anything approaching autonomy, not Tesla. Tesla requires a driver.
Tesla itself uses HD maps for things like intersections, traffic lights and so on. It's just not at the level of detail others use it for.
They’re also offering a commercial service. Which means figuring out operations, customer service, emergency protocols, working with local administration and so on. They’ve said a larger goal in Phoenix is to figure out how to perform and scale operations. The local regulations there are much more favorable. Until recently, Phoenix was one of the only (probably only) places where you could operate a robotaxi program and charge for it. California just recently approved it, so SF is where they’ll likely go next as they are already setting up everything there.
Ultimately, mapping is the not the constraint for them to go to new places. It’s the operations and regulations that they need to figure out every time.
Given that Tesla are the only company to have put something approaching autonomy into the hands of customers, that does seem to be the case.
What happens next in this thread? Someone points out that Tesla's solution is still far from perfect and claims that they're being highly irresponsible by having shipped it. Then I'd ask how many accidents have happened as a result of FSD beta having shipped to some customers already and they assert that Tesla isn't transparent with the data so we don't know. I'd point out that if we don't know of a single Tesla FSD accident so far, it can't be that irresponsible to have put it in the hands of a few customers and that it's been rapidly improving in the weeks since. It's the same thread, repeated over and over on here, Reddit, etc.
Tesla was the company that made electric vehicles successful. To your point about groups taking different approaches, I think Musk & Tesla do take approaches that will differ from others, and succeed partly because of their approach being better in some important way. I think they had a bit of an unfair advantage when it came to autonomy. They needed hardware that could be shipped on vehicles as soon as possible, which meant that it needed to be cost efficient & energy efficient. LIDAR's energy efficiency doesn't get talked about much, and I don't mean just the LIDAR itself but also the subsequent processing power required to make sense of the resulting point cloud. Each Waymo vehicle is an expensive tech demo. It's a very good tech demo, but over the years it's become evident that they're very hesitant to scale it up right now. I'm sure they'll eventually get there, but they are not a company focused on getting this done ASAP. Tesla are getting autonomy done with urgency.