Fame
Famous priests either work in the Vatican or did something totally awesome/noble/dangerous during times of crisis (or they were living in Biblical times). So, unless you want to be the jerk who prays for a war (in which case, maybe don't become a priest), your only real shot at fame is becoming the Pope, which is a pretty big jump from small-town priest.
Sure, it's possible to not be the Pope and be a famous priest. There are a couple famous priests right now. Ones who haven't survived wars or dictatorships usually did something like creating ground-breaking ideologies, starting famous charities, or are the president of Haiti.
Bottom line: It's tough to break into the famous priest crowd.