It's more complicated than that. In many cases, those in the cities that have decent public transport might not have parking spaces so they are forced into the decision rather than it being a choice.

In places where car ownership is possible, most people will have a car even if they use public transport for work. Why? Families are spread out, shops are in many different places, public transport tends to favour centralised areas like city centres and not other cross-city journeys and even a half mile walk to a bus stop or metro station is signficant if every journey is made that way. Children are often part of a club or whatever and in many cases, getting between all of these things is much quicker in a car than waiting for buses that don't turn up.

I like the idea of low-carbon environmentally friendly transport but it is a choice that in many cases is too big an ask, otherwise everyone would just do it. My car journey to work is 30 minutes. Doing the same journey on public transport would take at least 3 buses and probably 2 hours. Not happening.

Also, a lot of public transport seems expensive but I don't just want to jump on the "why is it so expensive in the UK and not elsewhere" because I don't think the economics are well understood.

Even in London, over half of households have at least 1 car

Which UK cities? A London year travel pass costs £2,568, so public transport is hardly cheaper either, plus it’s a whole lot less convenient. Unless you enjoy spending all of your time in an urban group think bubble with the only option is to use public transport to travel to more of the same.

While I disagree with GP about this applying to most cities in the UK, it's certainly the case that most people in inner London (Z1-3) don't own a car. The people who do own cars mostly don't use them for commuting. Kids seem to be the biggest reason people get a car.

Driving in London is expensive and inconvenient. Parking is extortionate, there's the congestion charge, road taxes, fuel duty and insurance. A car is something you get if you're reasonably well off or you need it for work (e.g. you're a tradesman).

Travelcards are expensive too - London is just expensive unfortunately. But that's a Z1-5 travelcard I think you've quoted. There are other ones and IME a lot of very poor people cycle, use the bus pass (£900) or get a Z2-6 (£1800) then walk from there, if indeed they even work in the centre. Also there are discounted rates for the travelcard depending on circumstances.

Do you live in London? Or visit?

In 2017, pre pandemic, there were only 166,000 annual travelcards sold.

No idea where your £2,568 comes from.