I haven't got time/patience for a full-on 2 page bullshit discussion about the semantics of what 'completeness' is, but I do have quick time for a bullshit comment:
Is completeness about how many things you can do, or is about how well you do them?
When I think of a 'complete' player, I tend to think of the latter; someone who has little/no room for improvement given what is required from their position or role in the team.