I took, naively, a product manager job at one place I worked, thinking it would finally give me formal control over the product that I'd been previously asserting through influence - very successfully - in my client-facing sales engineering role. Of course as soon as I got in the chair I discovered it was a highly-constrained clerical job that I was completely unsuited to. Managing tickets and a backlog; coordinating decisions instead of making them; writing interminable powerpoint reports; the most creative thing was putting together a process for the company to follow in formalizing its product roadmaps. I lasted six months before running away.
The function is quite useful in supplying some visibility into what's getting built and in managing conflicting priorities for a growing product, but one thing it is not is shaping or controlling the evolution of the product in any way. It's a sorting, filtering, and (if you're lucky) a data collection function, producing an auditable decision trail and an impression of maturity in decision making which helps the MBAs higher up sleep a little easier.