This is one of my main observations growing up with math: it's the moments of beauty and elegance that are the most exciting, but the grinding gears thing is also a necessity. They complement each other. For instance when you're just learning the basics there's a lot of these "wow what an insight" but over time you figure out that people have distilled it into a mechanical procedure, which also has some attraction to it. Something like quadratic equation turns the search for a pair of numbers that add up some one thing and multiply to another into a simple formula. You then use that mechanism to build ever more elaborate ones.