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?

Because they are seen as public transport. Technically they are only supposed to do so when working. Personally I prefer to have them in the taxi lanes as they are among the least predictable drivers.

This just came to mind, but they are a form of public transport commonly used by people who can't drive and might not be able to use buses, e.g. the elderly, the sick, the young.

But taxis don't have any of the key properties of public transport that usually motivate actively subsidizing its adoption?

* environmental friendliness
* low contribution to congestion
* high-fixed-cost cost curve

"You're annoying so you get to use the fast lane" feels like good short-term move but bad long-term :D

If taxi can, can Uber and Lyft? They are also some public transport.

100%, jackasses. They are better in a single lane than rush about in all directions