The problem with public transport is that it only goes on pre-planned routes. If you want to go elsewhere, you can’t without a car. And replacing all nature with rails and asphalt is a very bad idea.
Taxis exist.
A quick search suggests that here in the UK the average driver is spending up to £200 per month on their car (excluding any financing to pay for it in the first place). That much money would easily cover a monthly travel pass in most cities I’ve lived in, with plenty left over to pay for taxi rides when you need the convenience of door-to-door travel at a time that suits you.
I live in London zone 5, travelling to Zone 1 will cost me £267.30 monthly. One of my colleagues lives in Petersfield. His monthly ticket would be £613.70. You don’t know much about train fares in the UK, do you? If you live in Scotland and need to travel to London, it is always cheaper to bloody fly! Sometimes it’s cheaper to buy a car for one trip and then just dump it, or, even better, sell it and recoup your costs!
you don’t need to replace anything, the roads are already there. and if you wanna go somewhere super specific, just walk, keep in mind that if transport is more invested into, it will barely be different from car travel. the mild convenience created by cars isn’t worth the clutter that 10 times the volume of automobiles will create. also parking is already a problem now.
The problem isn’t the roads, but needing to create a route that touches every single road. Public transportation can’t really do customization, it’s a one size fits all deal.
My city has a door-2-door system of minibuses that are a bit like the missing link between taxis and buses. They pick you up from wherever you are and take you to wherever you’re going, they just pick up other people on the way too. It’s generally marketed towards the disabled/elderly, but I don’t see why it couldn’t be scaled up and be marketed as either a bus+ or a taxi lite.