I know your spitballing but I was enjoying exploring it because I think that such ideas are fun to play around with. Though, I think Bashir MD would end up like Trapper John, MD just due to the having to create problems that Bashir can't solve right until the very end, which feels like a very strange limitation on 24th/25th century tech. Kind of like transporters having to be broken every other episode. But, on the other hand, I love medical shows so I really want it to work.
it could end up something like “Diagnosis Murder” where he ends up having to solve a murder mystery on top of being a Doctor.