It solves the decentralized chicken-and-egg problem. You can't expect every appointment-place in the market to implement an appointment system that will work according to some common standard (which doesn't really exist yet), and the booking service isn't particularly useful until (and unless) a critical mass of service providers are compatible.
This approach, however, uses the "existing standard" (phone conversations in English or near-English) and can be eventually replaced by directly making an electronic booking for the places that will support it.
Offering a booking system to businesses is nowhere near sufficient, to offer this service to customers without being able to fall back to phone calls requires a near-universal adoption and that is an entirely different issue. This system can enable electronic booking even to places who don't offer electronic booking, won't offer electronic booking and don't want to do anything whatsoever to offer it, which in many domains means pretty much all places.
You can't force every service provider to use a web-based appointment system, but you can make such appointments without their explicit cooperation if they offer to do it over the phone.
This approach, however, uses the "existing standard" (phone conversations in English or near-English) and can be eventually replaced by directly making an electronic booking for the places that will support it.