> Uber does not determine the rate, the market do

Not true. Uber's algorithm sets the rate within certain profitability margins which are determined by uber, "the market" is very artificial since customers only ever see the rates that uber decides they should see rather than what some drivers would actually offer.

> Uber won't find drivers if the rate is too low, for example because it's lower than the costs, lower than the risk, or lower that the competition. Uber (and the driver too) won't find customers if the rate is too high.

Right... uber deliberately structures the market through their explicit control of the price. The price is only "too low" or "too high" with respect to uber's business goals not with respect to what the actual market would do.

There are other market players than Uber, and Uber is in no way a taxi monopoly. You could say this about literally any marketplace and especially about any taxi company (nearly all taxi companies have independent drivers-contractors, usually driving their own but branded cars - at their own expense, and with exclusivity contracts; taxis all over the world work this way), but only the more modern marketplaces are forced to modify their relationships. I both as a customer and a occasional driver hate this, thankfully I am driving in Czechia where no such law would ever pass, the traditional taxi lobby is not as strong - but they're trying hard.

> There are other market players than Uber, and Uber is in no way a taxi monopoly

True, but not relevant to my point which is that uber explicitly sets the rates, not drivers, and not the market. I understand why they do this, but it's simply false to say that drivers having the option to sometimes pass up on rides is the equivalent of setting their own rate.

Let's consider me, an IT contractor. I have a profile with IT staffing agency. They offer me contracts with a predetermined rate that I can accept or decline; I was offered an exclusivity contract for additional 5% income, but I declined. Why is me, an Uber driver so different that I am to be forced to be an employee?