Public transportation is not necessarily all that "cheap," it's often subsidized directly or indirectly. Cars are increasingly taxed (inc. fuel tax).

It's hard to legitimately say which is cheaper. Buses don't need their own infrastructure, but they do need roads and these are often funded by various car taxes. Still, they often need subsidies to run. Many also have subsidized rates for poorer people on top of that.

Transport is generally expensive. I don't think it can be taken as plain fact that driving cars is the most expensive method, especially outside of dense urban areas. If you gave those same subsidies to poor drivers, many would be able to afford to drive.

Excluding taxes, driving a low cost vehicle has a fairly decent cost per-km. A litter of petrol can take you 15-20 km in an efficient, small car. Untaxed, that's <$1. If you travel 500km per month, that's about $30. Add $110 for purchase and repairs (cheap car), $40 for insurance and we are at $170 per month. $5.50 per day. Pretty close to the price of public transport in many European cities, maybe less.

This is driving relatively little, but most car owners just consume more transport (travel more/farther) that public transport users. Also, more than one person can ride.

It also doesn't take into account for infrastructure costs though, but public transport's purchase price often doesn't' either.

I'm not saying cars are better/cheaper, just that it's not a clear win for either mode. Transport is expensive. If you have no money, you can't afford much of it. We subsidize public transport for poor people and could do the same with cars.

hmm I have not thought about it that way, but don't we subsidise public transport not only to make it affordable but also too use less energy for the same amount of people? Wouldn't fuel consumption per passenger be much higher if we subsidise cars?

Also most cities would not have the road-space to replace subways and busses by individual cars

Does that really add up? If the people who rely on public transportation are not the ones who will be able to afford the new services, how would the new services move money out of public transportation? Are you talking about the people who are currently spending their money on public transportation, but could in fact afford to spend it on some other, more luxurious transportation mode if they so chose? If so, isn't it likely that if they still choose public transportation, out of ideological concerns presumably, they will continue to do so in the future?

I'm not qualified, but I'm guessing that the money will mainly be moved from private car transportation to these new transportation services.

I kind of mixed up two arguments. My main argument was that there is definitely a need to invest into "yesteryears" public transport systems, because the new services are not affordable for anybody.

and the other argument is that new "high class" bus services take money out of public transportation, which is badly needed there, but as you said, this may not add up to much. (However I could see myself switching from public transport to self driving cars, so they can also be included in this argument)

But both arguments go in the same direction - that public transport is definitely necessary and will remain necessary in the future but is often neglected and in a really bad condition.