City governments would probably be the best choice to operate these transportation exchanges, where buyers (passengers in these cities) could meet sellers (drivers and taxis in these cities) on a centralized marketplace.
I like the proposed idea of avoiding network monopolies, by running them as an exchange with many suppliers for different levels of the supply chain. This would also apply to Amazon or AirBnB.
(I didn't find a non-paywalled version, so I'm linking to the tweet.)