This is a good point of view. Depending on your team or your org as a whole, it may be that you can manage communications just fine without one, but most of the time you can't. Also, in my org at least, the PM's main job is watching the budget.
My perspective, having worked with both good and bad PMs, is that a PM is a communication line aggregator.
In the example, every one of those lines consumes resources: time, context switching, misunderstanding, synchronization with the rest of the team.
A quality PM funnels all those lines through themselves. Their value is proportional to their ability to (a) bidirectionally extract, transform, and deliver useful information to both sides (developers and end users), (b) offload processing tasks that neither side is good at (merging similar requests, clarifying ambiguous requests, tracking down answers / requests for external teams), & (c) keeping a 10,000 view and coordinating tactical requests to align with strategic vision.
