That's simply not the same thing. The private limo industry is NOT a taxi service. Limo services aren't point to point, they're hiring a private car for the day or night. They're also FAR more expensive, and rely on reputation of the limo company.
Taxi services are normally dispatch services, with the drivers operating independently. It's VERY different from a limo service in about every way.
Taxi services are now suffering because of a combination of historic greed and anti-competitive actions. By that, I mean the sale of medallions, which brought in revenue to cities (greed) and made it difficult or impossible for people to start a taxi business (anti-competitive).
If cities want to eliminate the medallion program, stop the sale of them, etc, that's totally fine with me. But creating an unregulated industry to compete with a regulated one is simply unfair, and frankly possibly even unconstitutional. You can't make the laws apply to one set of people and not another. Uber is clearly a taxi dispatch service. Why should the law not apply to them, but apply to everyone else?