Taxis are part of the local public transit network here (and regulated by county officials).
§13(4) is about when to grant new taxi licenses, incl. a pretty detailed set of things for officials to look out for.
§13(5) is concerned with who is granted new licenses (established and new applicants, but folks need to be serious about running a taxi business; the latter precludes the 'on-and-off' Uber model), with an eye on avoiding concentration of power.
These things (along with all the other rules for public transit in general and taxis in particular in that law) make sense when considering taxis to be part of public infrastructure that just has to work, and not some investors' toy.
I can understand that investors and their minions running shops like Uber aren't happy about that, but luckily that was no concern when people wrote legislation on providing reliable infrastructure.
Uber was particularly tone-deaf here when pushing their all-American pitch about how they're taking on some evil monopoly (when in a city of 200'000 people, there's not a single taxi company commanding 25 cars. Most have 5 or less).
And why should they be called on this crap? Perhaps a limit on private-hire cars is part of the city's public transport and clean-air initiatives in some cases?
I've thought about it a bit more now, and those are valid reasons, IMHO. Obviously if the cap is there for arbitrary reasons or simply to protect incumbents then that's different.
If the city decides they do, they can simply keep Uber away just like Frankfurt and others did.
But for example: if the restriction is based on clean-air initiatives, why does it apply to EVs? Why do we have fixed spots for taxis to wait for fares, when we know can cheaply and easily call them up from anywhere?