The problem is idiots are actually influenced by advertising put out by the media, the candidates and superpacs. They’re too stupid to do a little bit of research.
So long as a significant percentage of Americans decide who to vote on based upon TV advertisements - we will continue to see the necessity of billion dollar political campaigns.
The solution is not more government control (and unconstitutional restrictions on free speech) - it is a populace that is better informed and disdainful of paid advertisements.