Only the western mainstream version of karma is supposed to work within one's lifetime. The proper spiritual interpretations of it usually span multiple lifetimes. Not a huge believer myself, but I agree with your conclusion, this kind of short-acting karma surely doesn't exist. As demonstrated daily by the many horrible influential people.
Yes it does, but even this version is not the quick "what goes around, comes around" what people casually think karma is, or what media like /r/instantkarma reinforces (albeit playfully).