Everybody knows what they are getting and that the usual "protections" from a government-licensed taxi service don't apply.
Really? I don't believe this to be true, and your argument from this point on fails because of it. Everyone doesn't know that they are not getting the protection of a licensed taxi. Maybe they don't know anything about Uber other than it provides what they understand to be taxis. Maybe their friend ordered the car and they think they're getting in a taxi?
And there are many regulations that people are legally not allowed to "opt out" of. For instance, I'm sure that many would be happy to build their house without following building regulations. Much cheaper. But they're not given that option. Many would be happy to accept a supply of gas from an unregulated supplier. All those rules add to the cost, and if you're prepared to accept the risks why not? Except the law is sometimes there to protect people from their own folly.