Big health plans stung by losses in the first few years of the U.S. health law’s implementation are seeking hefty premium increases for individual plans sold through insurance exchanges in more than a dozen states. The insurers’ proposed rates for individual coverage in states that have made their 2017 requests public largely bear out health plans’ grim predictions about their challenges under the health-care overhaul. According to the insurers’ filings with regulators, large plans in states including New York, Pennsylvania and Georgia are seeking to raise rates by 20% or more. In states such as Florida and Maryland, insurers are...