I have no view on or experience of LG, and will defer to Erik Mona's explanation.I'm going to show my age here and say that WotC ruined organized play when they started Living Greyhawk in 2000. Before that, you had tournament play with premade characters build for the module.
It was great. You got to play in highly themed parties that you wouldn't get in a home campaign (an afternoon of all pirates, all barbarians, all halflings or all whatever) and, with disposable characters, players focused on the role-playing aspects of the game instead of the character advancing aspects of the game. Just as importantly, because the characters were built with the module, you got to play an adventure that was actually about the PCs.
Plus, it was an advancement tournament, so once you got past the first round, the other advancing players were really, really, fun.
I've also never played an "advancement" tournament. All the convention tournaments I played scored teams against teams based on everyone playing through all the rounds.
But I agree that that sort of play was fun (although I never played a good D&D tournament in that style - the good games I remember were mostly freeform or Chaosium). It's a long time since I've been to a convention (as in 15+ years), and I'm surprised to hear that it's fallen out of favour.