I have experience in this area (sorry for the vagueness but would rather stay as anonymous as possible!) and some do come to therapy. It seems like a weird paradox but a lot deep down recognise their flaws and are deeply insecure about them, and so are actively trying to improve. That way, they can emulate their own portrayal of grandeur. However, it’s all on their terms - if a therapist was to say something they deemed critical, then they may not try as hard to work on it if they view it as an attack. There has been debate on previous threads as to whether Anna actually goes to therapy as much as she says (and she certainly doesn’t seem to have improved much) which may follow some traits of the narcissist.
Also, they are very very focused on how they are portrayed, even if they know it’s completely fake. Her image is extremely important, probably the most important thing to her, and she likes to portray him as a very rich man. By hiding him away, it helps uphold this illusion. Idk what goes on behind closed doors in their relationship, so we can only speculate. However, I would actually say a lot of the signs of how she acts from her public persona still point to narcissistic traits. She appears very difficult to deal with, won’t listen to criticism, has anger issues, and is constantly controlling the narrative. I wouldn’t be surprised if it was also this way at home.