"So no, it's not "utterly wrong"."
Yes, it is. Other ancient theories are crazily maddining wrong and certainly Newton's Principia is a shinning cathedral honoring the human intelligence but it still is utterly wrong.
Good you mention Asimov, since he was quite on the ontological path (against the pure mathematical path ala Dirac).
Now, forget about the numbers: it's about quality, not quantity. Newton thinks that there exists an absolute coordinate system and that things like mass, speed, length or time are therefore also absolute. Einstein demonstrates that he can't be any more wrong.
Ptolemy thought that the Earth is in the center of the universe and that objects in the sky circle around it by means of a dance of composed circles (epycicles and deferents) and it offers a magnificent math that "it's mostly right with many decimal places" and his model is also a magnificent show of human ingenuity. The problem with ptolemaic astronomy are not the numbers -ptolemaic astronomy can offer very precise numbers; it is the axioms: the Earth is not even near to the center of the solar system and there's no specific reason for orbits to be exclusively based on circles, so it is not a matter of how good its numbes are, just like there's no absolute coordinate system as Newton thought, no matter how good his numbers are.
As I see it, it's not that it would be mindblowing for the students to understand the basics of relativity or quantum mechanics but a matter of laziness from the teachers to find the proper way to teach them instead of "doing it as it has always been done".