It's how other characters in the books can easily identify them. They see the "ageless face" and instantly know they're Aes Sedai.It might be a defining feature in the book, but the question is can they identify them in the show in another way that doesn't require either vast makeup/GCI or young actresses who look to young an inexperienced.
Certainly not worth getting bothered over, doesn't change who or what they are.
Just because someone wears a green cloak, doesn't automatically mean that they're Aes Sedai of the Green Ajah. It could be just a nobody, who happens to have a green cloak. When someone sees an "ageless face" though, the meaning is unambiguous.