"In other words, 2-spool more parts, so more expensive."
Interesting. By "parts", I gather you don't just mean spools, but blades/stages, support bearings, airflow management components, fuel management components, gearbox accessories, etc, for specific engines from specific manufacturers?
Was this information something you were taught in the classroom, or did you take it upon yourself to count the parts?
Regards.
Q.