Seems like there would be a benefit to having a manager that is actually further from the problem itself. Less precious about details and more focused on universal principles.
What ex-engineer managers had was respect for the craft itself. You can respect the work of the team without doing it in the past.
I used to assume that. Until I met folks who seemed to be able to switch from micro details to macro "big picture" rather seamlessly. The extreme example of that is a Gates review[0]. Maybe that's why John Sculley never stood a chance.
It's more than respect for the craft, it's understanding the problem space.
What ex-engineer managers had was respect for the craft itself. You can respect the work of the team without doing it in the past.