How do casual gamers pay Riot any more than non-casual gamers? If anything, casual gamers tend to be more stingy with their money and less likely to pay out, as casual infers less of an investment into the game. Furthermore, rotating game modes are supposed to be FOR FUN, which by their very nature means that they're intended to be casual. It's the tryhard-gotta-win-em-all players that ruined the mode, not the casual players it was intended for.
Regarding which mode is superior, Riot had several years of URF, and each. and. every. single. time. the game mode devolved into Evelynn, Urgot, Katarina, Riven, Fizz, Sona, Urgot, Vladimir, and Annie, and a small handful of other bullshit champions that break the mode. The game became play one of them, or lose. There was no middle ground, because when people realize they can abuse the mode and cheese for the win, they almost always take it. So if a casual player played URF to play their favorite champ like Karma or Soraka on full blast, they would be relentlessly stomped into the ground, eventually driving them away from the mode.
ARURF, on the other hand, completely eliminated this cycle of bullshit by removing players' abilities to select their champion. There is now an actual chance to enjoy your game with other champs who aren't on the list above without being utterly destroyed 100% of the time. Sure, there's still champs who are insane, but the odds of running into teams who will always be superior to your team are now greatly lowered. ARURF is way better, and more fun, because games actually have a better chance at being fair.
As for the OP, in original URF, there were NEVER close games. It was stomp or be stomped with the same 10 champions always. I'm not sure what URF you ever played that was remotely considered a close game.