Viable alternative #1: Electric cars, powered by batteries, with 500 mile range and five minute charge time. Already demonstrated, as mentioned above.

Not viable, and not demonstrated large-scale and long-term. You've got possible constraints in battery manufacturing rate, problems with disposing of spent batteries, and a drastically increased load on a grid less able to tolerate it.

Viable alternative #2: Inductive connection to power distribution under pavement. Already in operation, as mentioned above.

And as people tried to explain to you, far too expensive to actually work.

Electricity in both cases provided by windmills, or water wheels, or hampsters on treadmills.

Great. Remember that we're dealing with a green grid here, with much less spare capacity. We can't just burn more oil to get more power, we have to do more with an inherently fixed supply of electricity.

Incidently, I believe that most public transportation systems require an explicit government subsidy. Certainly that's the case in the U.S., and I believe it is also in Europe. One may argue that cars are also subsidized, but that simply supports my argument that disentangling it all is very hard.

It does no such thing! Cars are also "explicitly" subsidized, and massively so. From construction to roadwork to filling up at the pump, never mind the massive unaccounted-for externalities. In fact, it proves that public transportation is no less viable than a car-centric system. And you have yet to explain why an explicit subsidy for a public good is in any way undesirable.