Agile Replacing Product Management
Question: "You're missing the big picture. Agile is gradually replacing product management and the product manager is being replaced by the product owner. Not so?"
This is not true. First, it should be noted that these beliefs occur only at software companies and only with Scrum.
Lightweight Software Development (rebranded as Agile in 2001) has been in existence since the 1960s and was never proclaimed as a replacement to product management. No cogent rationale for such a move can or was ever provided.
Scrum, a 1990s Agile method, includes a role with an arbitrary title of Product Owner which more appropriately should be named Backlog Manager.
The Product Owner was touted by some as a role that the Product Manager occasionally plays in an Agile/Scrum environment.
Nowadays there is recognition that the Product Manager role is wholly distinct from any product development role.
For more information, see the Transitioning from a Scrum Product Owner to a PMTK Product Manager article.