Thinking it though, it may work, but there is a potential problem. You're suggesting you expand the supply side in a surge by ensuring the the driver makes more money. So that means the company makes more profit during non-surge. But doesn't that open up an opportunity for a second company to come along and charge lower rates during non-surge periods?
Get rid of any incentive to act in the customer's best interest: Make sure that no drivers are compelled to go to less desirable areas, do a shift change right at rush hour, allow drivers to reject the rides they don't want, create no feedback loop, allow cash payments so they can pretend like the credit card machine is broken for extra tips, allow drivers to rip off visitors who don't know the area by taking longer and less direct routes, and don't increase the number of medallions ever.
There are other explanations / scenarios of course. I have a degree in economics, and, well, respectfully this seems more like a business/marketing domain issue. The change I was proposing would be at the same time too small of a price change and too muddled with other (real world, real time) variables to be well-modeled in the realm of economics.
Not sure about the low price elasticity. The article argues that demand for uber-rides varies drastically with price.
1) You're limited to a surge rate of ~1.25x, no more. (Maybe a few more percent if you pass through the safe rides fee.) Edit: and, per sibling, you're giving away business if you increase general rates.
2) You're giving up the extra profits you'd make at the very times when your product is most profitable and valuable, crippling the business model. It would be like if Facebook waived the price differential between general vs targeted ads.
Economics dictates as demand goes up and supply remains the same the price should go up. Once either supply goes up or demand goes down the price goes down. Uber is literally modeling economic theory.