Sweden deregulated its taxis in 1990. There is now no limit on the number of taxis (though drivers do have to pass an exam), and no restrictions on what they can charge. The deregulation did produce a big uptick in the # of taxis in Stockholm.
There are now some complaints in the other direction about the deregulated prices, especially because some less scrupulous drivers are trying to deliberately trick tourists into paying outrageous prices. Prices have to be posted in windows, so of course no Swede or tourist paying attention would take a taxi that charges $200 for what would normally be a $20 trip. But you only have to trick a handful per day to make it a profitable scam. Just need to get some tourists who either don't realize that rates are unregulated in Stockholm, who didn't see the rate sticker, or who did but didn't mentally convert the SEK to something they understand.
No limits on taxis as such in Sweden, there used to be but not anymore. However, you need to be licensed as a taxi company/driver and provide certain details on the cab, like price comparisons etc.
I don't know about Sweden, but here in Germany licenses are limited, i.e. there is no infinite amount of taxi license per city.