I don't see a problem with the last point actually -- as a taxi service company you need to pay for the car to go to the customer, then to go where customer wants. If the car is doing something else (delivering a package, driving another customer) while on the first leg of that, why would you expect not to pay for that leg? (assuming the car arrived within acceptable timeframe)

Problem of idling on multiple accounts can be solved by only paying out idle time by the company the driver ends up picking up a customer for or when the 2 or 4 hour shift ends. If you see driver idling on your time a lot and never picking up rides even though they are available, fire them like you would do with any employee.

As the second customer/employer, I wouldn't expect to pay time for the first leg while someone else was paying for it because routing may not be most beneficial to me/my customer. For example, the dropoff may be in the wrong direction -- I shouldn't pay for that, or the resulting extra time to doubleback.

Paying out idle time by the company that provides a fare makes sense, but requires cooperation between the employers.

But you control that by setting expectations, like driver must take a reasonably direct route after accepting request or arrive within a reasonable time. It is up to the driver then to decide if new request is on the route or postpone accepting until first commission is handled (somebody else might pick up that ride then).

I'm sure the devil is in detail though and we might end up with drivers occupied by route juggling when they should focus on safely driving...