Having also attended both public and ivy league schools in STEM from undergrad to PhD levels I can say from what I have seen there is a huge lack in mathematics education. This is especially true in the lower undergrad courses where profs see it as a burden to deal with in terms of teaching and the classes devolve into mechanistic / memorization exercises. very few teach students to reason with mathematics mostly prb bc 1 the profs are bad or disinterested teachers or 2 bc the profs have fundamentally other interests and are forced to each elementary classes in subjects they may mot have an affinity for or deep knowledge in- ie functional analysis or prob theory ... Once you get into the later classes math education steeply improves where fundamental questions are investigated and asked. i remember auditing a math physics class with 4 students and a prof al phd students - it was incredible and was totally outside of my area of research.

all this to say i think undergrad math education is poorly designed/ incentivized and run in my experience and leads to a huge loss of talent from the practice and art of mathematics.