We should not be asking whether most individuals today use higher-level math in their daily lives, because the answer we get will depend on the degree of math literacy of the people with whom those individuals must interact every day. The level of discourse is often dictated by the 'lowest common denominators' -- that is, the people with the least math literacy.
For example, freshly minted engineers who are surrounded by math-illiterate work colleagues quickly learn that they must avoid higher-level math if they want to interact successfully with others at work. Over time, the level of discourse of these engineers gradually drops toward that of the work colleagues with the least math literacy.
A type of "Gresham's Law for math literacy" is at work.[1]
The question we should be asking instead is whether society would be better off if more people had greater math training and literacy. Would our debates be more informed and higher-quality? Would our decisions be smarter? Would there be more technological innovation and wealth creation? Would society as a whole be better off if more people were trained to think creatively and critically with the rigor of higher-level mathematics?
I suspect the answer is yes.
[1] Gresham's Law -- https://en.wikipedia.org/wiki/Gresham%27s_law -- states that "bad money drives out good." In this case, unsophisticated discourse drives out high-level discourse.