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> About 80% of obese people with sleep apnea would be asymptomatic if they reduced to a non-obese weight.

Where are you getting this from? I didn't see anything like it in the study you linked, it doesn't match the general impression I've gotten reading other OSA studies, and it's unusual for lifestyle intervention studies to have a large number of people lose enough weight to go from obese to non-obese. Are you sure that you're not neglecting some other qualification of the population (e.g. mild sleep apnea, bariatric surgery)?

> For this subset of people, shouldn't insurers (and often the Public) encourage the patient to use the free, safe, and natural solution (eating less) before being dependent on an expensive machine?

No, because weight loss takes time, and there's nothing particularly safe about leaving OSA untreated in the interim. Weight loss is a fine thing to pursue for overweight and obese OSA patients, but deciding up-front to do that instead of CPAP is reckless. I agree with the authors of the study you linked when they conclude that "it is clear that treatment of OSA cannot be limited to any single strategy, but rather requires a multidisciplinary approach". Not every patient will respond to or tolerate every treatment approach, and the possibility of synergistic effects should not be ignored.