Higher math not only encompasses the theoretical side but also other areas like numerical analysis & applied math. Many or most differential equations, nobody knows how to solve. So we use computers to approximate solutions. Or you've got a matrix equation with 50 variables. Again, the methods people program into computers are interesting. The theory helps guide us- is there a solution? are there infinitely many solutions? Can knowing one solution help us narrow in on the other solutions more quickly?
Most (90%?) of Calculus students struggle to simply understand Calculus, much less the proofs, which some professors don't emphasize.
If A. you have the ability to see the lack of rigor in some Calculus books, and
B. you desire to see more rigorous proofs
then C. you are probably well suited for higher level math. I'm assuming you're in an engineering based calculus course & not a business calculus or simplified calculus course.
The students who complain about higher math, may have been just as likely to complain about Calculus when learning Calculus.