Sure, a push broom would work for the base task of getting the trimmings moved off the path, but then I'd want to disperse said trimmings somewhat evenly across the yard instead of just piled up at the edges. A push broom wasn't as effective to do the same while taking more effort and time. Especially since for the trimmings that went out into the street I need to get them up over the curb as well.
I used to use a broom before I got the leaf blower. The blower is way faster and disperses the trimmings more evenly across my yard than the broom.
I do end up using a rake though for leaves, as for actual leaf gathering usage the rake is faster and far more efficient at actually making nice, easy to handle piles.