are student councils really that important in japanese schools?

in anime I've seen way too much focus on clubs and student councils; how the position of the president is so respectable, and how serious and heavy their duties are.

so is this just an anime thing or true for actual Japanese schools?

like where I'm from, student councils were haphazardly made, sometimes through election but mostly through selection/nomination. it differs from school to school, but they really never had any serious duty. most of the schools don't have clubs or other things, but select members for extracurricular activities through teachers.