A handler with more than three dogs entered in a stake would mean more revenue for the club, it could be more hassle for the club and more competition for the other handlers, but it has nothing to do with the handler's amateur status. You are either working dogs for compensation or not, if not, how would the number of dogs you run alter that?
I also don't see it as a big problem that needs fixing, how many trials a year does one amateur enter more than three dogs in a stake? If it is a problem that needs to be solved, make a rule limiting the number of dogs anyone can enter in the amateur. Though I would be against such a rule, it at least doesn't try to redefine amateur in a way that has nothing to do with amateur-professional status.