Taxis are complementary to the higher-priority parts of the hierarchy. It's easier to commit to walking/cycling/public transport knowing that you can always take a taxi in a pinch. SOVs have the inverse effect - it's hard to combine them with other modes of transportation, and if you're already paying to own/maintain/insure a vehicle, you're incentivized away from considering alternatives.

One thing is that taxis don't need to be parked in urban centers, or if they are, their parking facilities don't have to be pleasant or convenient to peoples jobs. The search for a parking space increases car traffic and congestion. Also, parked cars occupy space that could be used to make it safer for pedestrians and cyclists.

Taxis (including uber, lyft, etc) greatly reduce costs for someone who only needs to travel by car sporadically, possibly making cities marginally more affordable.

I would assume because taxis offer the last mile service.

If you take a train to the burbs But you can't get from the station to your destination you may choose to drive the whole way instead of a short taxi trip, leading to more driven miles and more congestion.

Taxis don't need the same parking as a bunch of people driving to a destination. Less parking means denser land use which can mean less travel time and more green space.

Maybe because they do so many more miles and a lot of the carbon emissions these days are actually in the manufacturing process?