An anti-hero Bizarro only works where Superman has gone bad. “Us do opposite of all Earthly things.” Where Heroes and good, Bizarro is necessarily bad.
I think everyone is missing the real issue of a Bizarro film: the Bizarro concept is fraggin’ ridiculous to begin with. It’s juvenile and annoying. If Bizarro ever appeared he would have to be adapted to just being a confused clone of Superman who does bad things by mistake, and you have Conner for that anyway.