State Attorney Generals are usually charged with looking after the legal interests of their particular state, and then after larger legal interests and issues that affect a significant part of their population, such as consumer safety and fraud issues. If they were involved with direct supervision of locally elected District Attorneys, they would be expanding their scope to cover felony cases usually handled in the individual jurisdictions.
The way in which each level of justice decides how to handle and/or prosecute cases is completely different. The State offices tend to have larger guidelines, which they use as a litmus test when deciding how to direct state legal resources. If they were to supervising local level DA's offices, they would likely issue sweeping and general guidelines for the selection of cases to pursue. Local DAs would find their hands tied more often by procedural questions and both the conviction and prosecution rates might suffer a drop.