No, you just won't own your own car, you'll car share via a service like Uber. It would be way cheaper since you would no longer carry the maintenance and insurance costs for a vehicle. That's why it would lead to fwer cars on the road.
Don't kid yourself, if car driving gets cheaper people will do more of it. Or will you not be more likely to take a cab ride when it's $1 than when it's $20?
Autonomous car price will be higher, maintenance will be higher due to more costly electronics, insurance will be lower due to lower collision rate. Given these 3 unknown variables, how have you definitively concluded car price must be lower?
Finally, your economic argument is incomplete. When renting a resource is much cheaper than purchasing it outright, renting always wins.
Owning a car will be the domain of car enthusiasts, not the typical consumer.
As for maintenance/cost of hardware, I've heard that the LIDAR kit is under $10,000. Given how expensive new cars are and how cheap the same car becomes 10 years later, and given that that's a starting point, I'm not too concerned about depreciation cost.
In the western world there are also already so many suckers willing to pay the initial depreciation by buying new cars and then immediately selling them 5 years later for much less so they can pointlessly upgrade again, so the used car market will be filled with affordable self driving cars a few years after they come out. Like, you can already buy a car for less than the combined value of all its parts, because people put a negative premium on old cars. Why would it be any different in the future?
And given that LIDAR doesn't have moving parts, I'm not too concerned about the cost of maintenance. When you buy a 15 year old car, it's rarely the ABS or ECU or radio you need to replace, it's always moving parts like parts of the valvetrain, transmission, suspension.
And that's if you even use LIDAR. Tesla's cars apparently just use good old cameras. And we know how cheap and reliable those are
In the greater NYC commuter area, people already willingly pay more to live near a train station so they can more easily commute without having to "waste" the time they'd spend driving. (I'm sure this is true elsewhere) People are obviously already putting a price on this. Why pretend the cost of driving yourself is zero? It's absolutely not, unless your time is worthless.
Thought experiment: What's the longest commute you'd be willing to bear, if you drive yourself? How about if the car is self driving? If the answer to the latter is larger, you just proved you'd save literal money with a self driving car, not just figurative -- because you could move further away to cheaper housing.