A sheriff/judge/prosecutor who has to enough of what the local populace wants to see to get reelected may very well serve the interest of justice better than a

A sheriff/judge/prosecutor who has to enough of what the local populace wants to see to get reelected may very well serve the interest of justice better than a sheriff/judge/prosecutor who is beholden to organizational politics and political politics of the bureaucracy above them. This is very important in rural counties in states that are controlled by a couple urban areas and urban counties in states where more rural politics dominate state government because it allows them to have outcomes that are more just as the inhabitants of the county see it, even if they may seem less just from the perspective of the hypothetical average person in the state. Direct election of these officials basically provides a minority protection for counties that are in the minority in their state. Make no mistake, both local voters and state bureaucracy are more than capable of incentivizing non-just outcomes but putting that power with the local voters is more consistent with American values which generally prefer to have the most local level of government that can do something be the level of government that does the thing. TL;DR if you take the view that justice is relative to the wishes of the local community then having these officials elected by the local community makes perfect sense.