So you believe the booking is the most expensive part of running a professional car service? and that by automating the booking they would cut costs significantly?
In the UK, they have already automated it. Many cab companies allow booking by app, with a _similar_ experience to Uber (though with worse service, usually).
Importantly, they charge the full meter price as set by the licensing authority, and engage in the usual cab of tactics arguing about credit cards, taking sub-optimal routes and espousing disagreeable politics for the entire trip.
Really?