Product managers aren't idea people. They're not supposed to be, anyway.
They interview, the gather data, they build consensus around requirements, then deliver those requirements to development. Development is where the ideas happen.
Unfortunately, though, I think I know why you say this. Product management should not be about coming up with (read: dictating) ideas & implementation to product. It happens though and it's annoying as hell.
I think this is the case in a FB, What's App, or Tinder startup. But if you are in an advanced field like Medical, Law, etc. Then you need Product people with specializations to discuss with development and refine requirements.
They interview, the gather data, they build consensus around requirements, then deliver those requirements to development. Development is where the ideas happen.
Unfortunately, though, I think I know why you say this. Product management should not be about coming up with (read: dictating) ideas & implementation to product. It happens though and it's annoying as hell.