Except, it's not.
One of my favourite running themes throughout the show is that the Doctor's companions think of themselves as lucky women (and sometimes men) to run with the Doctor. After all, they are just 19 year old girls who live in council estates with their mother, or they are "just a temp" who thinks that just finding a husband will help her find value. There is the doctor who feels unloveable and the little redhead who just waits for someone to come back.
But through the Doctor, these women realize that they are incredible, important, invaluable. My favourite companion, Donna Noble, frequently exclaims that she's "just a temp" and what on earth can she do to help anyone, but by simply being with the Doctor, she realizes her resourcefulness and her compassion. We learn that the Doctor didn't choose her randomly; instead, she found the Doctor, because she's "the most important person in the universe," and she alone saves humanity from compete destruction.
There are other elements, of course. There is an episode where the Doctor comes face to face with the devil and that is scary. He faces real racism and discrimination on the Planet of the Ood. He loses control of his mind to an alien and that's terrifying. He faces his own loneliness, the knowledge that he is the last of his own species, time and again. For more than 900 years he's had to watch the people he love die, or lose their minds, or worse - forget him. These are heavy themes that act as a reminder: living forever and traversing all of time and space doesn't save you from very human pain.
But ultimately what makes the show so wonderful is that it is truth wrapped up in whimsy. While these immense themes provide the foundation of the show, the Doctor himself is the most whimsical character since Willy Wonka. He's lighthearted, forgetful, messy. He makes mistakes. He jokes. He has a strange eye for fashion and obsesses over Fez hats and Converse sneakers and leather jackets. He believes in the impossible because, more often than not, the impossible happens. He faces fear with curiosity and an adventurous heart(s), and he always hopes for the best and expects the best, too. He believes goodness is inside everyone, and that we all ultimately want to choose good over evil.
Post Script: This is my favourite quote about the essence of the Doctor from writer Steven Moffat:
It's hard to talk about the importance of an imaginary hero. But heroes ARE important: Heroes tell us something about ourselves.
History tells us who we used to be, documentaries tell us who we are now; but heroes tell us who we WANT to be.
And a lot of our heroes depress me.
But when they made this particular hero, they didn't give him a gun--they gave him a screwdriver to fix things. They didn't give him a tank or a warship or an x-wing fighter--they gave him a box from which you can call for help. And they didn't give him a superpower or pointy ears or a heat-ray--they gave him an extra HEART. They gave him two hearts! And that's an extraordinary thing.
There will never come a time when we don't need a hero like the Doctor.