I think it makes more sense. I think there must be a natural tendency for the two to grow together. After all, if one defines a particular output that the public sector needs to produce, then there is a presumption in a sense that it will be produced by a particular department.
The two ought to grow together. There's no point in having a department if it isn't producing outputs that anybody desires. The two do tend to march in step.
I think it makes sense to focus on what one wants to see produced by the public sector, rather than the institutions that are already doing the producing and therefore keeping themselves in business, whether they're producing anything useful or not.