Shinzon didn't irrationally go after Earth. The first scene in the movie establishes that's what Shinzon's motive was. Destroy Earth = Crippling the Federation. It's repeated throughout the film. Shinzon says this to Picard, Picard and Riker both deduce the reason why Shinzon would attack Earth.
The premise here is fairly ridiculous. Even putting that aside, simply replacing "Earth" with "the Federation" doesn't help the irrationality.