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.
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.
Furthermore, big companies all implement their own software or purchase a variety of systems, some of which have API's, all have different API's and none have open API's.
A system that can speak, universally, to every Salon (or even say... 60%) is actually considerably less complex than the universal API you're calling "easier".