Many in New York’s professional and cultural elite have long supported President Obama’s health care plan. But now, to their surprise, thousands of writers, opera singers, music teachers, photographers, doctors, lawyers and others are learning that their health insurance plans are being canceled and they may have to pay more to get comparable coverage, if they can find it. They are part of an unusual informal health insurance system that has developed in New York in which independent practitioners were able to get lower insurance rates through group plans, typically set up by their professional associations or chambers of commerce....