I can order a regular taxi via an app that is as good as Ubers, or hail one in the street, or go to a taxi stand (I doubt there will be an Uber at the stand, but there is nothing stopping them I suppose). Or I can order an Uber-. I'm not sure if I could actually hail an Uber on the street, but hypothetically if an uber driver was idling and saw I needed a taxi, I'm sure I could just take a seat and order the ride using the app from the passenger seat before we drive off.
Regardless of whether I order a regular taxi or an Uber, I can prepay, track it in the app etc. And regardless of whether I order an Uber or a regular car, I expect a nice driver and a reasonably new car (Not rarely a Tesla).
My point is: when there is no monopoly, the others can't afford to have an app, cars, or services that are worse than Ubers. Also, when there is no taxi monopoly, it's pretty natural that Uber is "taxi" like all the other taxi companies. They provide nothing that the others don't!
Depends on the market. In Las Vegas, for example, there is plenty of taxi competition, but the taxis only work the tourist zones. The reason the people of LV forced their local politicians to welcome Uber, above the objections of the taxi cartel, is because the taxis refuse to pick up the locals in the neighborhoods. There's no need to when they can make the same money, or better, being lazy working the tourists.
Uber and Lyft have been a godsend for people with limited mobility, the elderly, those who can't afford or choose not to have a car, and those who would like to have a nice night out without worrying about a DUI. Taxis are despised in Las Vegas. Their lobbying power is the reason the monorail system stops just short of the airport.
But that's not true. Uber doesn't fix these issues by being an "alternative", it fixes them by switching the incentives around. What this is about is "order a cab" vs. "hail a cab". By letting drivers opt into a ride, all of GP's issues disappear.
Of course you still do need competition once you're past that layer, yeah; taxi monopolies do sometimes offer cab-ordering services but those services still suck (Only available by phonecall with waiting time, no notifications, no prepayment etc). Simply removing the monopoly would not fix the issue entirely.