Most draftees during the Vietnam War did not go to Vietnam. Most of those who went had non-combat jobs. Flying a 1950's vintage high-performance jet at low levels was more dangerous than anything other than direct combat. Most positions requiring unusually long training also require that the trainee commit to spending more time in uniform, with the expectation of deployment. Bush, for instance, cold have been activated and sent to South East Asia and apparently did volunteer to go, but was turned down.
On the other hand, an enlisted seaman or airman would have next to no chance of being assigned to a combat position. Mind you, trying to get safe jobs didn't always work. John Kerry, for instance, says he deliberately chose to be a Naval officer in coastal patrol boats because he thought there was no chance of fighting. They then changed the rules on him, and he got out at his earliest opportunity.
As for Trump's medical exemption, all positions in the armed services have a minimum standard given that even a administrative clerk could find himself at sea or in a front line unit. If they just want non-deployable office workers, they just hire civilians.
Volunteers have to meet the same medical and physical standards as draftees, so if Trump had a disqualifying condition, he wouldn't have been able to serve no matter how much he wanted to do so.