In all honesty, I think you'd be a hardy soul indeed to make it to the middle of your life without HA these days. That's, of course, different to having a clinical anxiety disorder where it becomes your "ruler"... but then, that's the thing to think about.
It's somewhat unreasonable to wish health anxiety didn't exist, because if you were never anxious about your health, it would probably mean you didn't value it or your live or the lives of the people you love. It's just the emphasis you place on it and how much you allow it to dictate what you do on a daily basis (and by do, I mean thinking as well, it being a verb itself).
We can't control thoughts or feelings, it's true.. but like blanklook said, you can choose to notice them and be aware of them without training a laser-like focus on them. These thoughts and feelings are not the problem you think they are, neither are they "real" in these sense that a chair or a table or a pillow is.
Right now, you are you-here-now. Fear arises when your mind imagines you as you-then-there, somewhere that you are afraid of being. It feels as real as if it were you-here-now sometimes, but it's not real. It's just your imagination. Honestly.
I had extremely severe health anxiety with obsessive compulsive symptoms after the birth of my second son. It took a lot of therapy and a major commitment to living a life of value rather than fear, and some medication along the way, but you really can live a life that's not dominated by these fears.
I still have these fears. Why? Because I like being alive. I love my family, I love where I live, I love my work and cancer is scary, so I will always be afraid of it. The difference is that a fear comes and goes now, I do nothing with it and I get on with living this life I love. Turn what this fear means to you on its head. It's only there because life matters to you.