I'm a bit hesitant to let Uber etc just run free and amok in the market. I feel like there should be publicly available registration and verification data on all vehicles and drivers. There are very few, if any, other businesses that are free to run completely unchecked. Restaurants, gas stations, contractors, dentists, day cares, grocery stores, truckers, etc, etc, etc all have some degree of oversight, registration, verification for the purposes of trying to track and root out issues. Part of this could be tracking wheelchair accessible vehicles.
Alternatively, if the free market does succeed, and prices are higher for wheelchairs, then you might find people that specifically outfit their vehicle to cater to wheelchairs. And they might roam the city looking for wheelchair fares to optimize their revenue, potentially provided superb service (albeit at a higher cost).