You still need a phone to board. Or you have to cover the city in terminals where you can order that taxi thing. At that point might as well build the public transit stops.

Who says public transport can’t coexist in this imagiunary world?

But that's still not answering the main question: why do we need the system you're proposing in the first place? If we just start building more public transport and phasing out cars alltogether, it would result in better cities with faster commute times for everyone.

bridges for pedestrians or tunnels for vehicles.

1. Bridges are expensive. Tunnels are even more expensive.
2. They slow down pedestrian traffic massively, while it should be encouraged at any cost because it's the best way to make short trips.
3. They break up cycle paths, while cycling should be encouraged at any cost because it's the best way to make medium trips.
4. Bridges simply don't fit on city streets.
5. Lots of people have a stroller, or are in a wheelchair, or have heavy luggage, or are old, or have some other reason they can't climb up stairs. Adding an elevator on either side of the bridge explodes the budget.

There's a reason why almost all crossings in cities are level crossings. And level crossings fundamentally slow down car traffic, whether it's self driving or not is irrelevant, and at rush hour it means huge traffic jams.

because nobody can hack the streetlights. The internet is already everywhere. Luddites are irrelevant.

Hacking streetlights has very few consequences. Cities are well-lit regardless. It just makes it a bit harder to walk around. It might result in a few broken bones due to tripping on stuff, and a slight increase in instances of robbery.

But hacking the main way of transportation in a city would be disastrous. Thousands of people will literally die because of ambulances being stuck among millions of dead cars, and fire trucks not being able to make way to a fire.

Some things just don't belong on the internet. This will become more and more clear as techbros try to stick AI and IoT everywhere. After enough deaths we will learn.

In general, what you're proposing will not solve any problems that cities have (because it's fundamentally just cars, which are the main problem of modern cities) and will introduce a dozen more.