By far the most annoying myth I face when trying to discuss the pros and cons of various education techniques is the pervasive idea that everybody is a magical knowledge sponge and will go to their grave still remembering how to integrate by parts and every detail about some particular battle they covered in seventh grade, and therefore, if we slightly tweak a curriculum plan to drop something that was included on theirs we'll be stealing that knowledge from all the 70 year olds who will eventually have been on that plan.
Where this idea comes from I have no idea. Personally looking around in school itself it was plainly obvious this was all going in one ear and out the other for the majority of students even at the time. The better students retained it long enough to spew it out on the test but that was already above average performance. That doesn't mean there isn't still a certain amount of value in that in terms of what that knowledge may do to their brain during the brief period of time it is lodged in there. (I think there's a lot of value in just learning the "shape" of all this stuff, and perhaps having some index of what might be valuable to know.) But the idea that we can spend 15 minutes and a one-page homework assignment on something and expect that to last 60+ years is just nonsensical.
I mean, honestly, anyone over the age of 22 or so ought to be able to notice a distinctly sub-100% retention rate simply by looking inside themselves.
Yes, to a first approximation everyone with a normal education in the US has been present while some sort of trig was discussed. Not all of them, but still quite a lot of them, were present for the Taylor expansion discussion. The vast bulk of them have had it decay by 25, and there simply isn't anything to be done about that if you're talking about humans and not some homo educationous who mythically retain all knowledge they were exposed to even for 30 seconds just as the mythical as homo economicus perfectly rationally conducts all their economic business at all times. Perhaps they're actually the same species.