The definition of what is "core" to a computer is nebulous at best. Nothing stops you from having a SOC mainboard with some flash memory and an embedded process

The definition of what is "core" to a computer is nebulous at best. Nothing stops you from having a SOC mainboard with some flash memory and an embedded processor that can run on its own, with peripheral attachments to add in beefier hardware as need be. That is what PCI is for, after all. I think that may be one the largest failures of modern computing - we never built a hardware platform where just socketing (especially in a plug and play way) new processors, memory, busses etc was fluid and feasible. The performance penalties were always huge (albeit understandable with a monolithic virtual memory abstraction if you don't account for varying degrees of locality).