I agree completely. As the employee in the scenario, how do you influence your boss to buy into this new mindset of judging productivity and utility?
One trick: in weekly 1:1 meetings most employees will start by just discussing their current issues. Instead, start by talking about what you accomplished last week and its value, then move on to what's next. This is still a natural conversation (discussing the past, then future), but it makes your value and results much more visible.