Neither are the nationalized public transport systems they're competing against.

It's important to note that public transport systems are often forced to run unprofitable routes. Late night routes and paratransit are inherently unprofitable but improve accessibility. Of course, there are more unsavory reasons, usually political (for instance, the "Downtown Express" bus routes in Toronto were created to fulfill a political promise, and are vastly unprofitable as a result).

Ride-hailing services don't have this particular problem. They only need to serve based on rider demand. Yet at this moment they do rely on subsidies by VC money.

I think the issue here is just the 'size of solution' between private and public transport offerings. i.e. If you've got tens of thousands of people in a place - an underground line isn't a bad idea. If you've got tens - then that's not even enough for a bus. However an Uber driver (or even a pool route) is actually happier with the latter, as they're not having to compete with an underground. Different types of transport tend to be poorly integrated. Maybe airports being the only example I can think of where private and public play nicely together.

Don't forget to count the subsidized road infrastructure that Uber/Lyft use (and don't say "but gas taxes", they only pay for about half of road spending).