A fragmented executive power, like most states have, does solve problems stemming from the unitary executive, but also increases the difficulty of ascribing responsibility for bad outcomes whose source isn't exclsuviely in one bailiwick, complicating effective democratic accountability.

You could probably make a good case that doing this for just the AG is still a good thing.

(Of course, federally, that becomes both a major Constitutional change and raises the question of how they would be elected? The same Electoral College that elects the President? A separate electoral college? Direct election unlike the President? Of course, the first problem is one with any means of making the DoJ independent of Presidential control.)