What did Birdie say in All About Eve?
"Next to a tenor, a wardrobe woman is the touchiest thing in show business. She's only got three jobs: pick up clothes, press 'em wrong, and don't let nobody muscle in." Something like that, anyhow.
Stage managers are in Equity in large part to protect IATSE jobs, and vice-versa. If there were more crossover in responsibilities (if stage managers could be asked to perform building maintenance, for example), the unions would be constantly butting heads and producers would be playing them off against each other. Keeing stage managers in with the actors frees up additional work for IATSE members, forces producers to hire more people, and also promotes the idea that stage managers are artists, rather than technicians.