Depends on what you are optimizing for.
I can drive to work in 15 minutes, door-to-door. I used to ride the bus and sometimes I would be waiting that long just for the bus to appear.
The other factor is weather. Not many of the bus shelters around me (I’m in Austin) are air conditioned. Right now it’s 103F / 39C with a feels-like temperature of 107 / 42. Depending on your health, just walking around can be dangerous.
But I do think you are on the right track. I think public transportation in the form of buses doesn't make a lot of sense. But if Musk had been able to deliver on his promise of self-driving cars, then a giant city operated (or at least funded) fleet of small autonomous vehicles offering door-to-door service and route flexibility could change everything.
Cars are low to medium density transport, at best.
That wasn't true in the past. My father used to carpool with other teachers for 20+ years. I remember a lot of carpooling through the 1980s and into the mid 1990s where it fizzled out.
I would suggest, however, that self-driving cars would be fine for carpooling. Most people would have no problem carpooling with a self-driving car if it always picked up the same bunch of people every day. If I can commute in 35 minutes or take a self-driving carpool for 45 because it stopped to pick up 3 other people from my department along the way, that would be fine.
In a bus-optimized city, you'd be saying something like "Sure I can drive to work in 15 minutes, but it takes 5 minutes to park, costs $20 a day, and it's ten minutes walking from the parking lot to the office. Much better to take a bus that stops right across the street."
I used to think like you, that having car was a necessity, even freedom. Now I see it for what it is, a ball and chain.
Numbers taken from wikipedia.
Texas alone is twice the size of Germany - which is really crazy.
When an American says, "that is a three-day drive", they don't mean it will take three days of six hours a day with breaks every hour or two. They mean it will take three days of driving 12+ hours a day with 10-minute breaks every three or four hours. NY to LA is around 41 hours of actual driving per Google. So three consecutive 14-hour days just in the car, not counting getting a hotel room along the way, eating, using the bathroom, showering...
That many American cities are these monstrosities where car travel is the only way to navigate is because of poor design not out of necessity. The American car industry managed to halt the installation of public transport to a more effective degree than their European counterparts in the 50-60s.
This is not because Los Angeles is bigger than Zürich, or that it takes twice as long to cross the US compared to Europe by car.
In Zürich and Switzerland, they have highly effective trains. The US could do the same, but choose not to.
That said, US Metro cores are denser than anything in CH but have worse transit, demonstrating the importance of door to door analysis. Nobody wants to commute via mixed private and public transport.
It is really is quite remarkable. However, I think this is enabled by expensive high density apartment housing.
Americans would consider the apartment sizes inhumane and a supermajority of the population are locked out of our owning a home.
I don't know why you think there are fewer amenities here than in the US. What specific amenities do you think are lacking?
a 15 minute walk from me there are public baths(free, including the amazing Limmat river with crystal clear water), hiking(free), amazing bars, night clubs and restaurants.
Everytime(without fail) I mention how fantastic public transport can be using Zürich as an example, Americans mention that the "US is simply too big".
But that is not an argument! Build more lines? London also has a pretty solid public transport system(though not as great as it could be, due to how car centric the country is).
Car culture builds car cities. Once you have a car city it's nearly impossible to fix it... it's too big and expensive and low density to fix.
Where does the bus go? If you have dense city cores with business, commercial, and shopping it makes sense.
Living near Austin, I could take a bus to a place like the domain and have shaded walkways where I could walk to most shops without dying of heat stroke.
If I'm not going to the domain, I'm looking at businesses with huge parking lots strung along stroads. Walking from the bus drop off to a store might just kill you on a day like yesterday where it was 108F, and parking lot temps are closer to 130F.
Also getting to where you want to go over the huge spread out cities may involve waiting for 5 or 6 different busses.
And then hopefully your park and ride is being watched and you're windows aren't broken out.
Allow higher density housing to be built without opposition (for example up zoning 1 level should be automatically approved: single family home can be torn down to build a duplex, etc). Then reduce and remove parking requirements.
Once that's done density will just go up on its own and... cars don't scale. Traffic will absolutely murder everyone and they'll start demanding public transit.
However this whole path is killed via NIMBY.
I see so many new residential projects with small lots or apartments. That's great! But still the zoning forces just housing, so its just homes on homes on homes for miles.