The "key" to understanding the need for Core processes seems to be that those are the processes for which a company shall define KPIs.
That being clear to me now, I have the following question: is there any truth to the claim that core processes are those that are defined within the certification scope?
I would disagree with your conclusions.... core processes are essentially those which make product move toward the customer. (Sales, Design, Engineering, Purchasing, Manufacturing, warehousing, shipping...) Other processes are supporting or administrative- management, training, quality, maintenance, etc...
ALL processes are supposed to be measured or monitored for effectiveness and efficiency, not just your “core processes.” That is a frequent finding in audits. The supporting processes are to be measured as well. Frankly, they are often the ones where ineffective performance comes from, and impacts the main processes.