She doesn't seem to have an axe in hand. Carrie kept one on hand for breaking open beer kegs (they were made of wood then) and chopping down apple trees. She was an interesting character, but you can't just tell people not to do something that they want and expect that to work.

As I understand it, the Women’s suffrage movement used the temperance movement to get amendment 19 (women’s suffrage) right after 18 so at least something good came out of it.