Congress has begun the work of replacing the Affordable Care Act, and that means lawmakers will soon face the thorny dilemma that confronts every effort to overhaul health insurance: Sick people are expensive to cover, and someone has to pay.

The 2010 health law, also known as Obamacare, forced insurers to sell coverage to anyone, at the same price, regardless of their risk of incurring big claims. That provision was popular. Not so were rules requiring nearly everyone to have insurance, and higher premiums for healthy people...