But I'd wager to say the majority of the population that didn't consult a doctor due to a deficiency won't know this. (Unless, perhaps, when they studied something in the medical field).
This forced us to think about it and realize that the window was doing more than just refraction and was stripping out or absorbing part of the light and even though it appeared as the same light to us, whatever was being removed must have been in the spectrum of light not visible to humans.
So we all intuitively know this, but never stop to actually think about it.
The teacher primed you with "Why have you never gotten burned on a long summer drive?" and then you bought that as fact and backsplained it with some basic prism experiments, the backsplanation not really mattering once you buy the fact from the teacher.
In other words, I'm not sure what 30 second thought process you think the average person can walk through to replace a teacher telling you the fact outright.
Once you know a fact, people can "intuit" any explanation. Just talk to children and listen to their bizarre theories -- but I would not call that intuition because they cannot arrive at the original fact that way.
Besides, my intuition is the opposite. My friend was a truck driver and said he'd get sunburned hands. He always kept sunscreen in the cabin.
I think you're confusing the underlying theory with us encountering the question on the day we learned it and then dismissing the fact that we were primed with the current conversation to know the answer. What I'm saying is that once we had that knowledge about the underlying physics, the same question(s) could have been posed weeks or months later (with no priming) and we should have been able to figure it out.
Of course, given a premise "skin doesn't tan when sitting in a car", I think it's a good explanation for the subject.
It's still not clear to me if there are some types of glass that do allow vitamin D synthesis or not.