They're transporting people in bulk, that means some oversight from a public safety perspective is warranted
In some places, taxis are actually subject to some oversight from a public safety perspective. In those places, it's reasonable to be upset about Uber not doing those things well. In other places, they really aren't. There's really no oversight occurring. In those places, it is not reasonable to be upset at Uber, because they at least do minimal background checks in at least most places where they do business. Taxis are not as safe as you imagine, nor are taxi drivers (in any sense.) Taxi drivers who have been reported repeatedly as rapists continue to work, and rape again. With Uber, those people would get poor ratings and eventually be worked out of the system. It's terrible that it takes such a cold, impersonal, and capitalistic system to remove rapists from the transportation system, but that is still an improvement over at least some licensed taxi services.
Uber (as a corporation) is, drivers aside, no doubt made up primarily of sleazebags. But the situation is far more complex than "Uber is dangerous and irresponsible1!!!11!ones!" and complaining about it without acknowledging that seems sophomoric at best.
We'll see if taxis survive self-driving cars.
Of course they will. They will be self-driving taxis. The difference will be your contract terms.