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.

Building @kiwi 
Writing @ https://kanfa.macbudkowski.com/

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.