I've seen only a small fraction of the full service providers out there. But I cannot recall a one that did not use some variation on the two-call method for incall. The first 'call,' to name the hotel, could be voice, text, or email. But the second call, upon arrival, to get a room number, is always either text or voice. So a guy is gonna have to give up a phone number at some point. It's one of many reasons an anonymous, well-secured, hobby phone is so necessary. If your client is full-service, I don't see why the guys are balking.
But, again in my less than universal experience, massage providers are sometimes less stringent. Some will give complete location information days in advance. No phone call is ever required. So maybe some massage-only guys could get along without a hobby phone. If your client is a massage provider, that might be the problem.
And then there's the flip-side question. Why does she insist on a phone call or text before booking? If she insisted on a phone call, I could think she just wants to hear a voice for some reason. But what can she possibly get from a text that she doesn't get from email, apart from the phone number? It's unclear. When faced with demands I don't understand I get a little nervous. Maybe that is part of it.
Booking a first meet is always a bit fraught. I don't see the point of putting up roadblocks. But everyone needs something different to be comfortable. I've seen providers who use the two-call method and want to know the number you will call them from, but still won't give up their own phone number until an hour before the appointment. Maybe it's a timing issue for the guys, also.