People voted for FDR instead of Herbert Hoover, and that ultimately resulted in some pretty sweet policies. It wasn't perfect, but that is a prime example of a presidential vote being worth casting, in addition to more anarchist methods of bringing change.
There was a lot of protests happening at that time which really helped motivate the new president to actually do something, but if all those protestors chose not to vote, Hoover could've been elected instead, which seems... Not ideal?