If I had a dispatch company that phoned/radioed possible drivers in some round robin order, if driver number 4 always tends to decline I would stop wasting my time and my rider's time in contacting him again, after a point

Sure, but in this example the situation only happens because the dispatcher controls all the prices, if the drivers could set their own prices then they would have no reason to decline.

Economically the result is identical. The driver “sets their rate” above the market rate and drivers with lower rates get all the rides.

No, it is not at all identical because riders only get to see the prices that uber wants them to see rather than all the rates that would be available if drivers could set their own rates, thus "the market rate" cannot escape a threshold that is contrary to uber's business prerogatives.

First, there’s more than one app than just Uber.

Second, Uber is running the supply/demand auction system behind the scenes already. Prices are not fixed but dynamic and change in real-time based directly on supply and demand.

I’ve often brought up the app to check prices and decided not to ride for a while. Drivers do something similar.

> thus "the market rate" cannot escape a threshold that is contrary to uber's business prerogatives.

I’m not sure what this means. I’m sure Uber sets some reasonable floor on the price, but it’s more in the driver’s interest than their own. There are absolutely drivers who would drive for below operating cost of the vehicle because either they aren’t bothering to calculate it or they aren’t the ones actually paying for it (e.g. a car that is late on payments and soon to be repo’d).

Do taxi dispatchers track how often a driver accepts a request but never shows up? It sounded really common back when I was driving airport shuttles.

Not true - you can get logged out for inactivity, but you will never get banned or "fired"