Anyhow, isn't it possible to detect something like Huntington's Chorea by analyzing the blood of the applicant?
Yes it is but you wouldn't do the test unless the patient had symptoms (in which case they wouldn't get a pilot's licence until the test had come back) or if they volunteered a family history of the condition.
AMEs take chances all the time. They sign people medically fit on day x but they could start having angina on leaving the consultation and it wouldn't affect their licence until their next medical. We can't test for everything in every patient because
1. it would be prohibitively expensive and
2. tests are neither 100% sensitive or Specific (both false positives and false negatives) so some people will be labelled (and refused licences) inappropriately
Is there a question in the medical history section that says something like 'Is there anything that may affect your fitness to fly?' if you know of a positive family history and then say no then you are lying on the form.
This is a bit of a legal minefield but that is the best answer I can give. If I speak to a medical law specialist I will ask them.