I think you’d find that half or more would be completely unable to grasp the Twin Paradox, or double-slit even in principle, without the math. Probably the number would be closer to three-quarters, or even more if you factor in just how disinterested many would be. I like the idea of a world in which all 16 year olds are both capable of understanding your syllabus, and exposed to it, but I have doubts that we live in that world.
I do think that everyone should have access to such a syllabus though. More realistic if less transformative might be a program of teaching people very basic critical thinking skills. Use advertisements and Instagram posts to analyze deceptive languages and images. Show people that the world they think they live in, that’s projected all of their screens isn’t a very accurate representation of reality. Drive map-territory relations into them via the medium of political, corporate, and interpersonal deception they experience multiple times every day. Maybe half of them would get that, if it was made interesting enough to hold their attention.
Even less exciting things like seeing how the doppler effect led almost directly to the concept of the big bang is something that seems critical. That it's not (or, hopefully was not) a normal part of curricula seems odd. Even things like the mind boggling implications of the various conservation laws are just incredible. That topic is at least covered in lower education, but rarely if ever in such a way as to really elucidate how incredible these rules are, and all that can be derived from them.