I am not overly fazed by Superdad being a "part time hero" though I do have issues with how this was treated in the Lois & Clark mini.
My issue with Superdad is that he comes from a version (started by Byrne) that flew in the face of fifty years of characterization. The idea that Clark Kent was the real personality and Superman just a mask is not how the character had ever really been handled. Up to that point there had been basically two ways of looking at Superman; the stark division found in the Silver-Bronze Ages, and the more meshed version of the Golden Age where Superman acted like Superman regardless of whether he was dressed like Clark, unless he happened to remember that Clark was supposed to be a mild mannered coward. Byrne took everything fantastical and whimsical about Superman and stripped it away. When future writers tried to put those elements back, it never fit right. So far Superdad feels like a Superman to me, and the "regular guy" stuff has been balanced by his other, more Super qualities. But the fear of character regression hangs over his head and makes me worry.