I think if one is in the business of selling a fantasy which depends on a "look" or other attributes, you almost have to be transparent and share your face pic. I know some guys who are career-building professionals and where escorting is just a side hustle, they may be more reticent to share a face pic (unless they are completely comfortable and confident with their look).
Similarly, some escorts have asked for a face pic and once they get one, it's complete radio silence... so it works both ways. However, in my experience, most escorts do not ask for a face pic but having a visual description does help (which i always provide general stats in the first contact).