I'm not sure this is right. One of the very clever things Uber did was take advantage of a loophole in the hackney laws that allowed drivers to operate for hire without taxi medallions as long as they did not perform street hails. From the point of view of taxi operators who had long relied on this system to protect them from meaningful competition, this was a flouting of the intent of the law, if not the actual language of the law itself. They did not however, as far as I know, actually break the law.
Uber broke limousine chauffeur laws, not taxi laws. It varies from state to state, but generally you need a chauffeur license to pick someone up for hire. From what I understand there is generally no limit to how many might drive around but they are not allowed look for customers, the customer must find them.
The taxi industry was hurt the most, but it wasn't taxi laws that were broken it was chauffeur laws.
What? In the UK, private hire licensing is & always was a normal thing and the way Uber uses it is entirely normal too. It's not a loophole. They weren't even the first to allow booking without phoning.
Your comment seems to lack much in the way of fact.
They weren't banned in the UK. Or London. Their application for a license renewal was temporarily denied in London. They appealed, once.
They worked with TfL to resolve their concerns and were granted a new license - though slightly shorter term than normal. They're not entirely off the hook and will need to continue to show that they're behaving appropriately, but they're absolutely fine to operate now and that is not likely to change any time soon.
