I don't think any sport should be officiated by anyone who isn't part of the game - whether it be a hired official, or a player (and I think even this can be solved). In this day and age, the PGA Tour can figure out some way to have every shot played in a tournament either viewed by a hired official with their own eyes, or in some kind of "control room" where every shot played has a camera on it. There's only two-four people playing any given hole at a time. You could literally have a cameraman following every player in every tournament from the first tee to the last green and hire a bunch of rules officials sitting in a control room watching every shot. If a player has officially signed a card after a round, it ends there. I just think there's something innately silly about allowing someone watching a game on TV, who may even be on a different continent, be allowed to call out a player several hours after, or even the day after. There's got to be a better system than that.
Golf has always had a genteelness associated with it - its players are expected to be moral paradigms and admit every rules infraction, where my high school football coach used to actually encourage us to gouge people's eyes out in a pile to get a fumble (not quite, but you know what I mean). I respect that. I think it's silly to expect players to police themselves as well, though. With millions of dollars on the line and the chance to be known for the rest of sporting history, don't tell me some golfers wouldn't cheat if they thought the rule they were breaking wasn't inherently stupid and they could get away with it to win the Open or the Masters. I drive 40 mph on 35 mph streets every day like everyone else on the road. I'm not going to find a cop and admit that and ask for a speeding ticket.
Also, every sporting event in history has had some penalty call missed. A strike call screwed up. A missed charging foul. A missed holding penalty. A missed high sticking call. Etc. Even instant replay screws it up IMO sometimes. Some might say "well that's the reason we should allow TV viewers to get involved in golf." I think that just means we should make it easier on professional officials and leave the outside world away from it, then live with the best system we have and admit mistakes are part of life. Golf is a game. A game is a discreet phenomenon, apart from the rest of the world. And as for the argument that letting people call infractions in will promote participation and interest, puh-leeze. There's like 50 better ways to do that without letting some guy in a tank top watching a golf ball move 1/8 of an inch on his TV while guzzling beer in Yakima, WA determine who wins the Masters. It doesn't pass the common sense test to me.