Via is like Uber Pool, but more direct. While waiting, you only have less than a minute to hop in the car. Also the car only goes down major thoroughfares and moves only forward while in the car.
This has the effect of lowering cost per mile because the biggest input cost (labor) is reduced.
To me Via is more of a private, optimized bus system and an example of what Uber Pool could have been. Where I am Uber Pool is so hit or miss (really awesome because no one else gets in or awful because we crossed a major traffic intersection and have to back track two busy blocks to pick up a new passenger) that I avoid it.
Literal ride sharing like UberPool is the only actual cost advantage of apps over taxis, and if you picked the right vehicles for that you'd have a kind of bus/jitney system. Sounds good to me.
Lyft was released as an app to make finding a ride on Zimride easier, and quickly eclipsed Zimride.
Still, uber doesn't even pay when drivers don't have a ride, and they still lose a lot. I don't think you can be any cheaper than the subsidized Uber.
And I don't think you can save much regarding servicing. You already get very good prices with a few cars, or just with one if you carefully choose the garage. There is not much discount that you could get. Most costs will be gasoline, where discounts even for huge amounts are very small. So small that I know of several very large fleet operators in Europe which abandoned their own gas stations and instead had a contract with some gas stations to get a minor discount there.