Public transport is not a valid alternative because cars create endless neighbourhoods.
You can't make an effective transportation system with low pop density because few people will be able to get to stations on foot, and you can't make a fast transportation system because low density means downtown is very far away.
On the other hand, in downtown, cars are a big nuisance: they take most of the public space, they pollute, they are dangerous, etc.
And public transport takes twice as long because we've been focused on improving car-life as much as possible.
This is a good example of "things have to get worse before they get better", because in order to provide a decent alternative, we must, for some time, bite the bullet and ween off cars.
It's no wonder that public transport takes longer than private car travel: when you spend tens of millions of dollars on roads, when you illegalize crossing a street (jaywalking), when you optimize traffic lights to the flow of traffic, when you provide free parking, when you guarantee a minimum number of parking spaces per development, (and so on...), you've basically given public-transport the middle finger.
Public-transport and private (car ownership) transportation is an opportunity cost, and we've disproportionately spent our time and money on the latter. If we want to improve the former, then we're going to have to make these tough decisions to dis-incentivize private transportation.
You can't make an effective transportation system with low pop density because few people will be able to get to stations on foot, and you can't make a fast transportation system because low density means downtown is very far away.
On the other hand, in downtown, cars are a big nuisance: they take most of the public space, they pollute, they are dangerous, etc.