If you wait until you feel sick, you may find out you waited too long. It does happen.
The problem isn't whether it's a good idea, the problem is whether it's a good value.
I agree with your sentiment 100%, but it works both ways: your doctor will ignore a serious condition, thinking that it's something more common until a crisis happens.
This has happened to me twice - the last time, I went to a doctor with symptoms specifically asking if I should refrain from going camping in the desert. He cleared me to go, and the ensuing incident was life-threatening and cost much more than it should have.
Did going to the doctor help? He specifically stated that my concerns were unfounded, because "that's really rare" - he actually said that. (Talking elliptically to keep my privacy.) I had to go to emergency services and my preventative trip to the doctor was wasted.
I get my vehicle diagnosed yearly, and have all problems fixed before they become critical. My mechanic will tell me what's wrong, show me the bad/broken part in situ, give a firm estimate for repair, and guarantee the result.
My doctor will give me an opinion ("try this, and see if it goes away").
His opinion is backed by nothing. If he's wrong, I can't even get the cost of the appointment back.