Celine Dion does have a lot of fans. However, I don't think I would say she is a person without issues. She married her manager who is 26 years older than her, and who she began working with at age 12. Sorry - that doesn't scream normal to me. Not to mention her battle with an eating disorder.
I think it is very important to remember that while we may be fans of certain celebrities - they are typically only showing the public certain aspects of their personality. They make their money off of portraying certain images and come across as relatable to their fans. Unless you have met these celebrities personally, it is safe to say YOU DON'T KNOW THEM. Working in the entertainment industry is a really eye-opening experience. You get to see a lot of behind the scene behaviors and antics that the general public is not privy to. While initially I was a bit starstruck, I quickly realized that most of them are just like us but many with bigger (but different) problems than us.
All I am saying is that it is great to enjoy certain celebrities but don't be naive and think that means you "know" them. You know the side of them they want you to see.