I like the idea. It allows you to keep a "territory", without the need of owning the systems.
Spheres cannot overlap, and if a new faction choose a homesystem that is insde the sphere of influence of another faction, a hole in the sphere is created, containing the sphere of influence of the new faction.
(If you find any mistake in my English, please let me know via a PM)
(Really, I speak terrible English, so please, tell me if I make mistakes. I'd like to improve it a bit )