Very good point about (potential) stolen iPhones but your argument still applies to the current system. It's still a stranger in a car, they just happen to be sent under the banner of a company.

If the taxi firm itself implemented (or used a version) of this kind of service then that could be a great win for the firm.

Everything about anyone being able to join the network and become a taxi driver (from about the sixth paragraph onwards) is pure speculation; technically, there's nothing preventing it (well, aside from modifying the app to require more than hitting a button), but they haven't done so yet, and might not. Currently, they're contracted with black car services, so professional drivers who are probably at least as safe as a taxi driver (unless I'm horribly misreading this).

However, if they are considering moving in that direction (again, no proof of that), your criticism is really important to consider, and might be a pretty big limitation. I'm sure that there are ways around it, but only if the network of drivers is heavily moderated, with lots and lots of safe-guards built in. Also, not allowing children/teens to ride unless accompanied by an adult, and adding some sort of panic button to the app.