"You bet"? This is one of the core questions in human genomics/health research today and nobody has been able to make a convincing argument in general that your proposed approach would work.
Would you agree: The question being specifically whether in most cases necessary-even-if-not-sufficient genetic traits can be found ("genetic traits", as opposed to "genetic illnesses" since illness may not be the most likely result.) The problem being that although so far most of our exciting findings are of at-least-necessary genes (or plural genes, etc); obviously it's just these sort of cases that will produce high correlations and grab attention, so there should be a presumption of the equivalent of "publication bias." Necessarily, these will be the low-hanging fruit even if such cases are actually the exception, overall.
Of course, mere and relatively small correlations between disease and genetic traits are extremely common; but there are lots of possible explanations of such findings. In some cases 16 percent of all genes have a small positive correlation to a given disease, and "if everybody is at fault nobody is at fault!"
