Honestly, even trying to achieve the "theoretical ideal price" based on supply and demand is already screwing up with the market. Regular people are not like HFT algorithms, with infinite pools of money available and ability to turn opportunity cost into profit. Having a stable and predictable price is important when deciding whether or not order a taxi/rideshare at all.
(At least, that's my experience. I wonder what your data has to say on it.)
As a customer, I'd be happiest if taxi companies charged a rate per-km, that's calculated off their consumables + car amortization + some reasonable profit margin. I think drivers may be happier too - recent personal experience with myTaxi shows this. They offered a promotion in which the passenger would pay a fixed cost known immediately in the app, but which calculations changed every day or so. Some days, it would become a good deal for the drivers; other days, the drivers would be working at a loss. I had a lot of problems getting a ride when using this promotion, and chatting with the drivers revealed that they instinctively ignore those requests, as from their POV the profits are unreliable.
(At least, that's my experience. I wonder what your data has to say on it.)
As a customer, I'd be happiest if taxi companies charged a rate per-km, that's calculated off their consumables + car amortization + some reasonable profit margin. I think drivers may be happier too - recent personal experience with myTaxi shows this. They offered a promotion in which the passenger would pay a fixed cost known immediately in the app, but which calculations changed every day or so. Some days, it would become a good deal for the drivers; other days, the drivers would be working at a loss. I had a lot of problems getting a ride when using this promotion, and chatting with the drivers revealed that they instinctively ignore those requests, as from their POV the profits are unreliable.