I've yet to see the value in learning about proofs. I've haven't used them at all in my college calculus experience thus far.
I regret not paying more attention when trigonometry was discussed in highschool, as it is used frequently in my math, science, and engineering courses.
Algebra was a fairly easy subject for me but calculus caught me off-guard my first semester of college. It's similar in the sense that it just another set of rules you impose upon the more basic ones you already know in order to build an increasingly more versatile tool set for problem solving. The trick is being familiar with the tools and using your experience to know when to use which methods.
They aren't necessary, they just show how everything else you learned was developed.
