This is easily the best (and possibly only good) argument I've seen in favour of traditional cabs. The right kind of regulation can dramatically improve accessibility to people who are otherwise at risk of becoming marginalised.
Unregulated competition always has the risk of marginalising minorities because they might be too small to be an attractive market.
I think you are the one who doesn't understand how food supply works. Stores stock items which are popular - not ones which sell rarely. If disabled passengers are less than 5% of all taxi passengers, private companies might ignore them entirely because they are not worth the investment into their fleet.
Well if Uber or similar cannot serve this population then it would mean competition is not going to totally kill off existing services which do. He is already making a choice not to use public transportation not because it does not support his need but fails to meet his desire.
Not providing a service is not discrimination, refusing to provide is. Uber and others can simply have selection criteria listed for owners who support disabled or even large people. If there is a market for it I am sure people will step up.
Unregulated competition always has the risk of marginalising minorities because they might be too small to be an attractive market.