Why is it so uncommon to find material that shows students how everything is connected?
A recurrent question from students is why are polynomial so important? If we shown them how these are related to real functions and to differential equations, they would be more interested in learning I think.
Otherwise, processing polynomials is just a mechanical ability. The same applies to second degree equations. Many, really many students know how to solve them, but it's quite rare to find those who know what real world phenomena they describe.