Unless you are rich taxi/uber is not an alternative to car ownership. (rich call it a limo). Those are alternatives for when something else covers most of your needs but once in a while it is lacking. If you own a car you need a 'i'm drunk' option. If you take transit you need a 'i'm going where transit doesn't or is too slow' option.
I'm not saying taking an uber everywhere is an alternative to having a car. It's part of the system. There's public transport (tube, DLR, overground, trams, busses), there's rental bikes, rental scooters, there's uber/taxi, there's walking. You use the "car ownership alternative" (or a combination of them) that works for each given situation.
I think the point the OP is making is that the burden of car ownership in somewhere like London is already very high. So those who can do without by and large do. The remaining folks who do still have a car do so for a reason (job, primarily) and are unlikely to get rid of it just because Uber exists.
