Unless every person agrees (not just the person that requests the ride), this could be illegal in many states.
In Canada this would be illegal, and many customers would not agree to being filmed.
"By using this service you agree to be filmed. If you do not agree, feel free to use an alternative". Seems like it would work as nobody is forced to Uber, no?
I'm not saying that this is the outcome people want, BTW. Just that it could be the one they get.
This is coercive and is as such already pretty legally shaky. It would probably fly in the US, but that's not the only place they operate.