Republicans are legally barred from bringing any challenges to voting lists and Democrats perpetrate and benefit from industrial scale vote fraud. Why would they call the AG’s attention to something like that?
Most vote fraud complaints are in the primary, Dem on Dem and R on R and in local non-partisan elections. So the technicality you mention is irrelevant most of the time.
For example, the most fraudulent election I’m aware of is the nonpartisan race for Chicago Alderman with Sandi Jackson (wife of Jesse Jr) where Obama’s mentors (Stroger/Beavers/Partee orgs) fought against Operation PUSH. In that election both sides conducted massive vote fraud, which made it more fraudulent than where just one side commits vote fraud.
Obama’s vindictive US Attorney targeted the Jacksons but did not touch the vote fraud issue.
When a prosecutor brings a case, he represents the people. He does not (technically) represent a political party.