We might also ask this of the introductory college physics course, which will be taken by a lot of non-physics majors, who will never take another physics course, but will for the rest of their lives read popular articles on gravity and black holes and have [mostly] no idea what is going on.
There seem to be several pros and cons. The first pro is to satisfy the above mentioned curiosity. This applies also to physics majors, who out of curiosity will begin thinking about it on their own. In fact, I never met anyone who didn't begin thinking about it and trying to figure it out on their on, but they generally have to wait until graduate school, IF a GR class is even offered at their university. Many don't.
The cons would seem to be of the nature of how much time it takes and how much preparatory work needs to be done. Clearly a course in GR cannot be squeezed into half an hour of lecture. Some compromises would have to be made, and virtually no GR experts have been willing to make any. GR must be approached through the field equation, Riemann curvature, tensors, etc., even if it means a kind of Egyptian priesthood in which few are taught hieroglyphics.
Suppose a simple, fast half hour approach to weak field gravity were available. Would it be so damaging to the minds of future physicists that others should be denied it? Bear in mind the future physicists will damage their own minds anyway, thinking about the subject while they wait.
I will propose the first answer to start the discussion. My answer is yes, it should be taught, and if clearly done it'll take about half an hour. OK, an hour at most, but well worth it. I submit a possible approach in the paper linked below, which explains how to read a funnel diagram, and how to understand the factor of 2 in light bending as half due to time dilation and half due to space expansion. It even includes an optional section deriving the relation between time dilation and space expansion. It is completely correct and consistent with GRT as far as I can tell.
Here is a careful development of static gravity and the Schwarzschild solution following the steps of the field equation and Schwarzschild's method, using the same principles, the same physics that is, but avoiding tensor formulations by various tricks. It's not exactly short and simple, but I'm thinking it may be comprehensible to more advanced high school students. Please comment if this subject interests you.
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