I think simply owning a car will be such a signal, similar to how owning a plane today is a mark of the super-wealthy. There will be "automotive Boeings" that produce cars for transportation companies, boutique shops that produce them for the wealthy, and not much in between.

Yes, this is already the case in China and I suspect in many places around the world. In Shenzhen, taxis are very cheap and available within 100m around the clock pretty much everywhere. Even if you drive on average 1 hour per day which is very unusual in a high density city, owning a car would probably be more expensive then always taking the taxi. Yet, a lot of people still purchase cars (mostly luxury brands).

I suspect this is the case almost everywhere in the world. A car's purchase price + gas + maintenance + taxes easily surpasses what you'd spend on taxis, even in a 5 year period. The keys to car ownership are convenience and the emotional aspects.

Taxis don't go everywhere.