There USED to be a good reason for many of them. Then they started being used to cull competition, raise prices and barriers to entry for no other reason than to make more money. This is why Taxi Medallions in certain cities are worth MILLIONS.
Good points. Let's look at Taxi Medallions. Now, when they were originally implemented the idea was that there were too many taxis on the roads clogging things up. So let's restrict the number, move more people to public transit. Except that the cities keep expanding and issuing NEW medallions becomes extremely hard because you have these hugely wealthy taxi companies that hold most of the medallions that realize that every new medallion issued reduces the value of their existing ones.
In NYC at least as a result you have 'livery services' which are essentially taxis that aren't allowed to stop for 'flags' on the street. IE you call one up, negotiate a price over the phone(or internet) and the car will come pick you up at a designated time and drop you off. There are additional complexities involving airports, of course.
By the same token, for the longest time the only vehicle that was considered 'suitable' for a NYC cab was a special stretch Crown Vic, apparently under concerns about leg space that assumed both the driver and passengers were all NBA athletes.
As is, new 'taxicab of the future', a Nissan NV200, has some issues because it's not handicapped accessible.
Personally, I think it'd be cheaper to simply subsidize a number of cars to have the ability and use them on a call out basis so they're no more expensive than taxis. Same with apartments, really. Requiring 100% of apartments be wheelchair accessible is more expensive than simply giving the population in wheelchairs free handicapped apartments.