Do doctors see a lot of patients with obstructive sleep apnea?

I do. I do, but my practice is limited to sleep disorders, so there is selection bias. Primary care physicians (pcp) see a lot of people complaining of difficulty falling asleep, difficulty staying awake, and of generally unsatisfatory sleep quality. Some of these are sent to sleep centers for further evaluation and some are managed by the pcp. 10% of people suffer from insomnia; 9-24% from sleep apnea.
Yes. As a primary care and sleep specialist, I see a lot of patient with sleep apnea. We use the Berlin Questionnaire to screen patients as well as the Epworth Sleepiness Scale to quantify peoples level of sleepiness.