For small private planes? Slots are hardly ever the limiting factor.
Taxis are more like private jets than Airbuses carrying hundreds of pax.
While taxis aren't as good for society as buses, they still reduce the total amount of car infrastructure required. The slot comparison doesn't seem apt.
No they don't. They choke up the most costly piece of car infrastructure - road space in the very centre of cities.
If I drive myself to somewhere in the centre, my car will sit there using up space while I'm doing my thing. If I use a taxi, the same car that delivered me will serve other people while I'm doing my thing.
Of course it would be even better if I used public transport, but I'm not going to do that because public transport is uncomfortable at best.
In the absence of terrible laws, it'll be stored somewhere that's more space-efficient (e.g. in a multistory car-park) compared to a taxi cruising around the main streets looking for fares.