The preponderance of a given condition is not a function of having insurance (though complications thereof can certainly be increased by NOT having insurance). And has already been factored in by actuaries into policy pricing.
The biggest issue is that we see health insurance AS insurance, not amortized healthcare costing.
> There has to be some way that the insurance company can make money on the odds.
That's the thing, they see an opportunity to increase profit.
A few comments on that, as someone who has worked in the industry of developing software for health insurance claims management and benefit processing:
1) insurers are incentivized to deny claims, often talking about how "unfair" it might be for "them" to have to pay for a treatment. The irony is that "they" are not paying for anything - the risk pool is. Those premiums were calculated based on actuarial assessment, plus insurer overhead calculated in. What they mean by "them" having to pay out is that we cut into their profits, as they don't refund money to risk pools if the entirety of the pool is not used - they keep it, in addition to the admin overhead.
2) insurers have been known to be outright unethical, if not illegal in denying claims. Some prurient examples: denying Heli EMS for car accident victims from the scene to a trauma center because of "lack of pre-approval" (sorry, as a paramedic I am not "hold[ing] for a nurse consult" as I call an insurer to decide whether they are going to deign to pay for this patient's transport, and retroactively canceling coverage for "failure to disclose a pre-existing condition" that was actually unknown at the time of disclosure, i.e. "You were seeing a physician for maladies X, Y and Z. You had not been diagnosed with anything at that point, but later were, and maladies X, Y and Z were symptomatic of that. Ergo, you had that condition at that time, though you did not have a formal diagnosis, and failed to disclose that you had it. Accordingly we are voiding your coverage for breach of contract".