The primary purpose of public transport (within an urban area) is reducing traffic. The vast majority of people can use private vehicles just fine, and if traffic is not an issue, the rest can use taxis. Subsidized ones if necessary.
Reducing traffic is the primary goal. When there is less traffic, the city can reserve less space for streets and parking. That leaves more space for the purposes people are in the city for. Also, areas with fewer cars tend to be more pleasant than areas with heavy traffic.
> The vast majority of people can use private vehicles just fine,
Roughly half the population of the UK has nowhere off road to park the car and only enough space in the road to park one or sometimes only one for each two dwellings and you risk someone else taking the space if you move your car. This means that while it might be literally true there is nonetheless a substantial number of people for whom using a private vehicle is not just fine.
Half the population of the UK lives in areas where public transport has enabled limiting the space required by traffic. In some other parts of the world, similar situations have been resolved by removing excess houses, making more space for traffic.
Also, private vehicles include bikes and scooters, which are often more appropriate for urban settings than cars.
People living in terraced houses in the middle of my home town would be rather surprised to hear that I think. Many of the houses in question are at least a hundred years old, they were there and the roads they are on were there long before "public transport enabled limiting the space required by traffic". And anyway the remark is not about traffic, it is about where the cars sit when they are not in traffic. And who is going to decide that your house is an "excess" house? It's not as if it is easy to find a place to live in some parts of the UK.
> In some other parts of the world, similar situations have been resolved by removing excess houses, making more space for traffic.
Reducing traffic is the primary goal. When there is less traffic, the city can reserve less space for streets and parking. That leaves more space for the purposes people are in the city for. Also, areas with fewer cars tend to be more pleasant than areas with heavy traffic.
Congestion and pollution are secondary issues.