> Very few engineers want to maintain relationships with customers, interview users to identify potential features, manage leadership, play politics for resource allocation, and so on

Ah, so that's what a product manager is supposed to do. When product managers were introduced at a company I worked at, they did very little of any of that. They certainly weren't speaking to customers. They weren't technical, so they weren't managing our Jira tickets. And "managing leadership" fell mostly on our managers' plates. I think the PMs mostly had meetings, talked to leadership, talked to engineers, wrote documents, and presided over the (now very long) sprint planning meetings.

I can imagine product managers that did your list of things being a lot more valuable.