I think the reason most Americans think voting is important is because the government will effect them and their kids, and even possibly their grandkids! It could also be because the political climate is very extreme, on both sides it’s either extreme liberal or extreme republican. If a person is a liberal, they wouldn’t want an extreme republican and vise versa.
Sorry if you don’t like this, or if you needed a better/ different answer! but hope this inspires you or helps you!!