Who decides the categories? For example, what would the category say next to a cert for Amazon? Google? Netflix? What would the cert say for Slack (who pivoted from one industry to another)?
Attempting to embed additional visible info in the cert requires some centralized consensus, and trusted validation that certs being provisioned match the consensus. And all of this occurs despite the continued fact that end users do not even look at the certificate information anyways, so we’ve deployed a new central body with a bunch of administrative overhead and not moved the needle on actual security.