And, a good PM also says "no" or "can it wait" or "ok, if you insist, but here's the downside" to folks on the other side of the line - customers, senior management.

Yes, this. Dealing with the upstream is the part of product management that most engineers severely dislike. Also, dealing cross-functionally with all the parts of a product team that aren't engineering (are marketing up to date on the launch? what's our ops plan?) -- and reaching out across teams to collaborate and build new products. I've worked with some great tech leads who were almost entirely PMs in terms of what they did, but that left them with very little time to actually write code.