Here are two reasons I think are important, there are more but these stand out. (1) Teaching is hard, and the amount of training you get in teaching higher level maths (rather than the just learning higher level maths itself) is very limited. (2) intuition in maths will lead you on a merry path to very wrong ideas. There are functions that are continuous everywhere without a derivative anywhere, Russell's paradox, classically zenos paradox, etc, etc. A big part of higher level maths training is in being precise with what you mean so that you can learn to do proofs and not trick yourself. I think a synthesis of these approaches is the sweet spot. Be precise but show applications to motivate the material.