Why is a for profit corporation the right instrument here? It seems to me that wanting to join together for political speech doesn't need a profit motive, since there is another motive. Does America not recognize provide any manners for organization that are not for profit without needing to be charitable?

A 'foundation' in the Netherlands (where I am from) would serve perfectly. And it seems to make sense to me to bar for-profit organizations from influencing elections because of the inherent conflict.