Uber already works this way here in the UK and in my opinion it's the only fair way to charge for rides. I'm totally ok with paying for the ride I actually took (taking into account traffic and diversions) so that drivers make a decent living.
As long as the price estimation is working properly the profit for the driver should even out in the long term.
And, if the route taken is unreasonably different from the optimal route, I can complain to Uber and get a refund.
So yes, while drivers may be incentivised to take longer routes, they can’t do it without being exposed.