Feh. It's his school, he can do it however he wants. If he wants to be choosy, he can be choosy based on whatever he wants. If he wants to be choosy based on whether or not someone irritates him on the phone, that's his choice.
I know one instructor who will only teach based on whether or not someone he knows and trusts refers the new student to him. No walk-ins. Not even a public store-front.
I know of one school which basically doesn't answer questions from phone calls beyond some basics of where to find the published content. You can go online and see reviews of classes and what the basic curriculum will be. If you don't show up with the right equipment, they'll sell or rent it to you.
I came across one club, years ago, who claimed to teach African or Nubian Martial Arts (think "ancient Egyptian" or the like). They categorically refused to teach anyone who wasn't ethnically black. Is that racist? Yes. But it wasn't a commercial club. They can choose their students based on whatever they want.
Me, personally, I'll have phone conversations if I have the time. Otherwise, I say that I can't talk and goodbye. Show up to my class and if I don't like you, then go away. I also don't teach kids when I teach western martial arts. My club. My way.
I get what you're saying. It's the standard model for public sales/service institutions. If I were running a Jiffy Lube and I wanted to make lots of money, then your way is usually right.
But most places, during most times in history, martial arts instruction, indeed most any knowledge and skills based instruction, is a sellers market. The seller gets to decide, based on their own criteria, whether or not the customer will get the training.
So if he wants to be Foghorn Leghorn, "I say, I say.. You bug me son. Go away" that's perfectly acceptable.
Peace favor your sword,
Kirk