I personally think the idea of piyutim shouldn’t be taken lightly. They were created with much thought, effort, concentration. Ba’alei Ruach Hakodeh, and through Ruach Hakodesh. There are some works that deal with the mystical meanings and references to their words. In fact, I recall hearing that in some (maybe all) every letter was weighted, and contain sublime lofty and mystical thoughts.
Someone opening a machzor and ripping out a page here, a page there, at will is like a child “working” at the hood of a car, pulling out (needless) pipes, wires and belts.