The problem is that the Department of Justice is part of the Executive Branch, and due to the burgeoning of the Imperial Presidency over the past several decades, that means that as soon as a new President is voted in, he can order the DoJ to change all their priorities to match his.

Our system doesn't have to be this way, even with the federal/state split; it doesn't even have to be this way with the designation of the DoJ as being within the Executive Branch. It's taken a lot of erosion of norms and flagrant breaking of laws to get to the point the US is at now.