Unsupervised and left to my own devices, I tend to spend my time on what I actually think is the most valuable contribution I can make. Selfishly, perhaps, because that tends to lead me toward what I find to be the most fulfilling and enjoyable work. This tends to upset some people, because my maximum effort is not funneled toward advancing their immediate metrics. But others get it.
In my experience, just doing work you are told to do is the surest path to burnout (at least for me). If I am allowed to pick an area I concentrate on, I remain engaged and excited about the project and spend more hours per week on it. From manager's POV is that so bad?