I live in Singapore and this is already happening here. In Singapore to own a car you've to get a certificate of ownership that can cost around $70-$100k and you've to bid for this. Ever since Uber began to get popular here we've had rental companies (who only rent if you become an Uber driver, essentially partners of Uber) try to undermine the bidding system by artificially boosting prices.
It has never been easy (or cheap) to privately own a car in Singapore but the situation right now is exactly like you mentioned in your comment.
However I'm also a resident of the US and I don't think it's gonna happen over there anytime soon.