That does not describe my experience with taxi drivers at all. They speed a lot and customers expect them to speed when they hurry somewhere. (I do not live in USA)
This might be due to the economical aspect of a taxi ride. The base fee starts at 7.00 euros sometimes, just for walking into the taxi. I don't have the exact fares data, but although they are earning additional money during the whole ride, for short rides it's clearly more remunerative for them to get to destination as soon as possible to be able to take another one.
You also haven't taken a UberX ride from looks of it. If you did, you would realize that they never ever speed and are very courteous in their manners!
I know it sounds strange - that professional drivers speed like mad dogs and are at many time disrespectful while random people like you and me are better/sane drivers - but it is what it is. Uber does a great job weeding out bad drivers through their rating system - unfortunately cabs can't do that..
On the other hand, I do not really get UberX. What is the difference to any other taxi I order by using an app (and there are many such apps now in most cities, at least in Western Europe)?
I have used UberX too and most drivers told me that we were not accepted for Uber, so they were driving for UberX in the hope of making it to Uber later. That would also explain part of your experience, i.e., the speeding. For a professional driver, speeding, especially when driving a customer, should be an absolute no-go.
In any case, I am very sorry for your experience with the American police. I have never had any encounter with the American police but I am also afraid of having an experience like you had. And as a guest in the US, there is not much I could do but to be as obedient as possible … :(