What makes the "Product Manager" role tricky is every person and every organization has a wildly different sense of what they do.

You argue that there's not enough room in a person's brain for Software Engineering and Product Management, but "Product Management" often includes planning, strategy, coordination, vision, culture, anything vaguely leadership, and general "adulting". To call all of that mushed together a "discipline" makes no sense.

Skills like coordination and vision are just as orthogonal from each-other as software engineering.

As a result the best PMs are often those who know what control to give up to make the role / team function better.

I've even been on teams where engineers seem hesitant to organize fun events because it may be perceived as stepping on a PM's turf, which is absurd!

I think teams and PMs would benefit from splitting up the role. I'd love to see the creation of roles like "Associate Producer" (as borrowed from the film industry) that have a primary task of keeping things running smoothly without a strong focus on creative or technical leadership.