Having an entire separate org whose sole job is to create backlog items inevitably ends up with 100s of items, 15-30% of which are "high" priority. Many of these will have out of date specs by the time engineering can pull them in.

I would much rather have product folks embedded in the engineering team. That way they can be working on making sure any issues on deck to be worked on next have up to date, clear requirements, and issues are prioritized correctly.

Having product people separated into their own organization almost always leads to a "throw it over the wall" situation.