Indeed, the relativity of core vs supportive vs generic in business lines is often overlooked. I give examples of payment processing for e-commerce, where it's always "generic". But for Stripe it's core as that's what they do.
I think I also found a great example where within a company something they (and the others) consider "generic" could become core out of serendipity. This example is AWS. The "biggest bookstore on Earth" invented the public cloud, something that IT industry giants failed to do. If Amazon would just blindly keep considering their infrastructure management as "generic supportive" subdomain, it won't ever happen. That's what great companies do.