I feel like we’re thinking about this 90degrees apart. I think about the underlying constraint implementation as being the main goal. You’re talking about the primary key generation as being the goal.

Interesting observation! I was trying to center the discussion on the non-SQL parts in my original

required=A query must include this column.

index=The set of all index columns defines a unique row and other code may make optimizations given this assumption.

additional=Table implementation code takes explicit action on this data if present.

And I felt like you were focusing on the specific actions such as a primary key being defined.