I don’t know anything about combinatory logic, but your question sounds similar to “why study push-down automata if we already know that turning machines are Tu

I don’t know anything about combinatory logic, but your question sounds similar to “why study push-down automata if we already know that turning machines are Turning complete?” Maybe I’m way off base in drawing that parallel, and if I am I’m curious why. Aren’t systems like these used to explore the hierarchy of computational power? I’m assuming that studying systems with less power is how those lines are drawn. Is that not the case here?