but that is when you see a doctor
When you don't see a doctor, then filling out a box for your race doesn't exactly help much, either, because you don't know which risks you have inherited from which branch of your family.
And "race" doesn't cover it. If you're Amish, (or your parents are and you left the community and are now atheist) then you are very clearly "white" in terms of race, and you ticking that box won't help anyone diagnose you with anything. If, however, the doctor sees you, and can ask you where your parents are from, they'll know that you are at higher risk for specific diseases.
A doctor will only be able to screen you for diseases you are at higher risk for due to your ancestry if you tell them about said ancestry; not if you are forced to decide which "race" you are to be counted as without even knowing about risk factors.
Perhaps "race" works for you because your genetic background is so homogenous that you can easily decide on a "race", but that's not exactly common.