VERY interesting post, point, and question!
As a child and teen temperatures were taken, and enemas given where you stood, errrr so to speak. It didn't matter if it was the sofa in the living room or den, a bed in a bedroom, or in my case, we had a large, about adult waist height, 2 sided book case that was in the den. Interestingly, if you imagine the height of an old style exam table, that would be a good comparison. Often, depending on what needed to be done, overall the top of that bookcase, a flat surface, was covered with a towel or blanket and used to give us our enemas, etc.
I agree, I much preferred a soft comfy surface like a sofa or bed, but, again, I think it was an element of the era. Such things were so common and accepted back then that tables and the sort were indeed frequently used. My friends would relate stories about the kitchen table, etc. Looking back, I often wonder if our parents in that era did that to emulate the effect of a doctor's office exam table to kind of set the mood and environment in our heads as kids, and make it seem more "real" to us; more "official", so to speak.
It's going to be interesting to see other responses from children of the 50s/60s/70s on this one.