This isn't even an irrational vision, it's illogical.
Let's assume this scenario comes about. Doctors are being physically coerced to treat people; but let's face it, most of them end up being ferried between the residences of wealthy individuals and politicians, because those are the people that matter. With guns pointed at their heads, doctors are told they must see patients and perform operations. The enslaved physicians realize that if they all died, there would be no one to provide healthcare. They all go on strike and say "Go ahead, beat us, torture us, kill us--but without us in supreme working condition, you won't have anyone to treat your upper-middle-classes." The shoe's on the other foot now, and suddenly the "draft" doesn't look like such a good idea because--wouldn't you know--the military draft teaches soldiers the skills they need to know, whereas the "healthcare draft" requires its doctors to already be familiar with their craft (and unfortunately, they're the only ones who know how to do it...
).