One question the city probably can't answer is what disabled persons in the taxi are supposed to do. If you strictly enforce bike lanes the result is probably the rider needing to walk a few blocks. If the rider is disabled, that could actually be a huge burden. Since I've got an 80+ year old disabled parent with a walker this is an issue for me that does compete pretty aggressively with my support for bikes.

First of all, the walk would rarely be more than half a block. Bike lanes go down a small number of streets, so one can usually unload on an intersecting street. Not ideal, but ...

... bike lanes are not the only thing that creates this issue. Any road that lacks parking, with or without bike lanes, will have the same problem. Even when there is parking, all of the parking spots may be occupied. In both cases, people may have to walk a few blocks. While they may be grouchy about the lack of (sufficient) parking, you don't see many people blaming motorists for placing a burden on the elderly.

Finally, it is always possible to make accommodations. Having a carve-out for loading and unloading taxis will do far more for safety of everybody than letting people stop anywhere in bike lanes. It is also possible to have exceptions for people with disabilities, as long as non-disabled people don't abuse it.