Yes, they do have a right to ask for a pic because there are no laws saying it is illegal. Same thing when someone asks for your salary; they can ask it because it's not an illegal question.
"generally hot people chose to date hot people" -- Yes, and as you pointed out: it's when they want to date. Escorting is hiring a sex provider, and is not about dating. It's a business transaction after all.
Nonetheless, Either party can withdraw from the business if they don't feel engaging with each other.