When they catch on to one, there are still a dozen others.
Are there? If so, one wonders how they got anyone to serve at all.
That aside, there is one important point to the situation to consider. The OP posited a WWII type of war. While the war in Viet Nam was bad (in terms of national mobilization), it was a neighborhood brawl compared to WWII.
The Viet Nam conflict saw about 500K US soldiers participate, out of a population of about 200 million. WWII, OTOH, saw a total U.S. mobilization of about 16 million men out of a total population of 130 million (which includes EVERYONE — men, women, children, elderly, etc.). In other words, just about everyone who could fight in WWII was sent to do so.
In a true WWII-style mobilization, the draft boards are going to pull everyone they can. High cholesterol won’t keep you out. In Viet Nam, there were plenty of other people who could serve instead. In WWII, that wasn’t the case. If the US had to suddenly mobilize 16-25 million warriors, you aren’t going to get out with simple cholesterol tricks, pretending not to speak English or other such tricks.
The Wolf