Given how insurance works, this possibility should concern people more.

Insurance is a bet. Like all gambling establishments in Las Vegas, they need to take in enough money to cover overhead, pay staff, pay off the (financial) "winners" and still turn a profit.

If your genes guarantee you X problem, it's a "sucker's bet." There's no money to be made covering you. It's effectively charity to let you buy coverage for a pittance knowing you will get a big payout.

Even if you work for an insurance company, having a genetic disorder automatically disqualifies you from purchasing a lot of their policies.

That's basically what would happen. So you would have any of the scenarios below

1. you pay higher because the info you provided them made them think that you are likely to be correlated with people that have genetic trait x which is linked to conditions w, y and z

2. you pay as normal, but when you want a payout because you suddenly have a condition for which you are genetically predisposed, you don't receive anything or receive a really small amount of money (small enough that they will make enough profit from you, but just enough that you won't sue immediately)

This is already illegal though, directly by the Genetic Information Nondiscrimination Act, which passed 420 to 12. I'm not pro DNA collection by any means but this argument gets tossed around a lot and it's clearly undesirable to everybody, and we can change/set laws to prohibit it.