It could work the other way to: new analysis on your DNA could reduce your premiums. As such, I don't think it's unreasonable for some people to want to submit their DNA.
Figuring out increasingly accurately who is going to get sick breaks the entire point of insurance as a cost pool based on the inherent uncertainty of who is going to be a net payer and who a net payee and at the limit your costs gets increasingly close to the cost of care + cost of administration with the added negative that the insurance industry that has taken your premiums for decades can decide they like your money too much to part with it and keep it depriving you of care perhaps because the care that may keep you alive is experimental.
It is in all of societies interests to make the temporary gains you describe simply illegal and to reconsider the utility of insurance as a method to pay for medical care in the face of increasingly predictable risks.
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