The point of brown shirts, at least as I understand it, is that they help you to gain control of the state, since either you don’t hold office and therefore don’t hold authority over the cops, etc., or you do hold office and the cops, etc., are mostly more interested in preserving the institutions that employ them than they are in a revolt. Fascism doesn’t just happen when a fascist takes the highest office (if he even does), he needs a dedicated base of power to overthrow the government.

That’s not the only thing brown shirts did, but it’s important to note that once Hitler was sufficiently close to becoming an autocrat, the brown shirts were perceived as a liability due to their independent ambitions and were liquidated in an agreement with the actual German military, which was expedient for gaining their cooperation.

I don’t have the firmest grasp on this history, admittedly, but I think this much is solid.