In multiple European cities now I see taxis being allowed to use the bus lane (while of course regular cars are not).

What's the policy justification for this?

I like it. 

When I need to move fast to e.g., catch a plane, I take a taxi. 

Taxi drivers need to have a license, so they pay back some money to the city for utilizing the bus lane.

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Btw in Warsaw, electric cars can also use bus passes since they want to incentivize ppl to buy the less air polluting cars

IMO because:
- rich people would just buy this access and use the lanes even when they're not in a rush,
- taxis are shared and utilized most of the time vs. private cars that move from point A to point B and get parked.

If the goal is to charge for priority access to give a way for people who really need it to get priority and raise revenue, why not decouple the "taxi vs car" aspect from the "paying for priority or not" aspect?

I am a public transport maxi and never seen it causing any problems in Warsaw (can't say for other cities). On crowded streets buses go every 2-4 minutes, even 60 taxis per hour wouldn't really impact the traffic.

Some people never take a public transport, so at least they take a taxi instead of blocking the roads while looking for a parking spot.

The point of bus lines is that it incentivizes people to have a viable alternative to riding/driving a car. If taxis makes this less viable it will end up leading to the same problem as if everyone rides a car. Public transport demand has to be induced

I can vouch for this, saved my ass many times. Literally skipping line for reason eh and disincentivizing using owned cars which are not shared. More of those lines I think and we generally push cars out of cities, at least those which are not utilized 100% whole day.

Is it possible that taxi drivers are in a hurry?? People with regular cars may only be traveling