I entered software engineering by making simple web tools for my job in customer support. For a while I continued making tools for the department and those were some of my most effective projects because I knew the domain intimately and what the pain points were and the mentality of my former colleagues so I knew what kind of UX would work for my users.

So I don't think it's managers who need this so much as engineers who can do something to help, because as a colleague put it, laziness is a powerful motivator for engineers.