But wouldn't that same minority still exert influence on politicians once elected by promising to steer business capital into specific districts or by offering post election employment or by favors to family, friends, associates? If that minority is indeed exerting undue influence on politicians through campaign contributions, once denied that avenue, won't another one simply become the favorite way of buying influence?

Personally, I think that if buying influence is as common as some might believe, it would be better to diminish the amount of influence available.