Municipalities require licensing for taxi services because the taxi drivers are conducting the actual business transaction -- agreeing to transport the customer for a price, whether pre-agreed or subject to a meter reading, at the point of pickup within the municipality.
Most municipalities also require background checks for the drivers and company owners, and have safety requirements for the vehicles, as [a means to ensure customer safety | a revenue generator].
Passengers, however, are unscreened and unknown. They might come in from a phone call, or they might hail a taxi on the street.
Most of the risk, both financial and otherwise, falls on the drivers.
So, along come Uber, Lyft and their ilk, conducting the transactions online (thus, outside the municipality) and essentially reversing the standard cabbie/passenger dynamic: the passengers are pre-identified (to sign up, they needed a cell phone, a credit card and a valid address to go with it), and the drivers are unknown (except to the companies, which do little or no effective screening). The vehicles used are unlikely to meet the requirements for taxi use, and are often flat-out unsafe for drivers, passengers, or bystanders.
The companies start doing business anywhere they like, and fight against the requirements -- only if challenged -- with funds from their financial backers.
Municipalities are not happy about this, for both safety and financial reasons. Taxi owners and drivers, most of whom have invested considerable time and money to clear regulatory hurdles, are understandably upset at this end run around the law.
Imagine if Internet gun sellers showed up doing business in NYC or Washington, D.C. and claimed similar exemption from the local (highly restrictive) laws...