Some good points and reminders here, thanks for writing this David. Personally I think the Product Owner is optional to attend but having said that, no one from the team should be excluded.

I think for the most part Product Owners can stay quiet for the delivery side of a stand-up because that isn't their primary focus. However, I like Product Owners to set aside a few minutes at the end of the delivery stand-up to ensure the rest of the team is across the discovery work they're doing (e.g. customer feedback and data insights) that way the team is always up to date on the latest information from its customers and stakeholders.