What Uber forbids is building up such a clientele from customers it brought through the app.
Depending on the local jursidiction, they might be absolutely free to do street pickups.
For example in Finland someone driving for Uber could pickup someone from the street.
There is no ability to use the Uber platform for hailed or other ad-hoc rides, they must be ordered through the platform and all payments must go through Uber.
Uber provides the commercial insurance to drivers they need when carrying passengers, for example (pretty sure they do this in all areas they operate, but I'll wait with bated breath to be told they don't in Bulgaria). If a taxi driver who also worked for Uber picked up a hailed ride it would not cover them.
Uber provides some insurance in _most_ countries they operate in, but it's quite often the case that this is not enough and that other insurance (usually specific for their classification e.g. Taxi Driver insurance, or VTC insurance) is required. So your point on insurance is quite moot.
What's actually interesting is that some of Uber's competitors do have a street-hailing functionality, where the app essentially works as a virtual card terminal for hand-hailed rides. Cool!
My point is even the French classify rideshare drivers and taxi drivers differently, per your own admission.
What I wanted to establish here is that 1) Conditions for driving for a ridehailing platform differ massively by city or by country. 2) I do not know of any countries which classify "uber drivers' as any form of legal classification. There might be a distinction between taxis, and other forms of "private for hire transport services", which is again an argument for treating these as independent contractors.
You've made some reasonable points for sure. The universal difference between traditional taxi drivers and Uber drivers that I want to reiterate is that truly self-employed taxi drivers are paid directly by customers, whereas Uber drivers are always paid exclusively by Uber. That, I feel, is a very important distinction when comparing their employment status.
Here in Ontario rideshare drivers and taxi drivers both have different legal status. Most legislation is on the municipal level but there is provincial law as well that makes the distinction.
A customer can hand me cash and nobody gets a piece except the government. An Uber driver cannot accept cash or payment outside the Uber app or they will be fired.