In NYC Ubers have contributed to increased car traffic, so definitely a net negative for congested urban life and global warming at the same time.

"contributed to increased car traffic" = "lots of people use it"

Yeah that was part of it, but the same study found a lot of it was due to circling blocks around already high traffic areas without passengers waiting for fares. In that case, that added traffic would be from people not using the service, but the service requiring a physical footprint in the city in the name of an empty uber vehicle anyway for it to function, if people were to use it.

You can argue buses and trains also need space, but you can fit way more people into a bus or a train before you need to make square footage available for a second bus or a train.

The per-mile cost of rail or bus is much, much lower than a car or SUV.

If they are so mismanaged that they can't offer drastically lower prices, then driving them out of business and replacing them with better management seems like a great idea.

that competition is fairly small. in the US, there is very few cities with good public transport

Yes, I can accept that it's region specific. It's the case in London, for example. Uber has made central London traffic worse. And that would be the case for many places outside of NA.