Of course we built a road system - without paved roads cars are mostly useless. We have build rail systems in the past as well. The problem isn't unsolvable by the nature of the problem. It is unsolvable because you can't get the right people to make long term investments in it (don't look to government - anyone who tries will be voted out eventually at best the system changes course from one okay system to a different incompatible system, though more likely they just stop investing).
They don't live a good distance from work because they want to they do because they can't afford to do otherwise. If you told one of the multitude of people who commute via car they have to spend 5000 on a clown car and an an hour to their commute which amounts to 500 hours annually or 20 days spent commuting they would be in your front yard with torches.
Instead what you need is enough housing to bring its price low enough for more people to live closer to work and enough transit that people want to use it not a clown car mandate.
When you have successfully convinced most people to commute differently you can start to limit cars not before.
In US public policy we are the kings of the Grandfather Clause. Every model of ICE vehicle known for drivetrain longevity will suddenly become coveted by the road warrior class, and that 0.1% of the population will compete over them for the next 20 years while peak mileage and recharge speed of all-electrics goes up.
My sedan has better handling than the roadster I had as a young man. When I tried to relive that in my 30's, it didn't pan out. In the sedan, I won't die instantly in a t-bone or any accident with a truck. Antilock brakes are life.
Things change and antique vehicles become quainter by the year, and at some point you'll have a brief period of mourning and switch without another fuss. But you have time for it to happen organically.
Or, hybrid vehicles will stay legal for a long time, and you will just own one of those and leave the rest of us alone.
1. One do-everything car (short and long trips without pre-planning)
2. Living in an apartment so no overnight charging.
Even with 200mi range, you have to ensure there are chargers en route because they are still sparse and it still takes a long time to charge the car. Gas vehicles still win because in most places, you can expect a gas station within 50 miles and the time penalty is 5 mins vs hours.
Sparse city charging infrastructure also mean makes charging much harder.
We're getting better but imo electric cars in the US at least are still limited to wealthier folks with houses that have charging stations and some city dwellers in nice apartment complexes. I hope we see a good sub 30k electric car soon to shake things up.
For a while I did make a tiny car and a SUV work, but I had to drive ~100 miles a day for work and even then it just barely worked out.
Anyway, some actual data. Most cars spend the vast majority of their time going exactly nowhere: https://www.racfoundation.org/motoring-faqs/mobility#a5
The average trip is 8 miles (same source, both in the UK. You can find data for your country. Might also look at https://www.sciencedirect.com/science/article/pii/S019126151...)
Plenty of time to charge from a domestic charger, and no range issue with current electric cars (which have >200 mile range).