Since time immemmorial, two forces have been at odds: the Radiant (or "Sentinel" in older texts) and the Dire ("Scourge"). The manifest in physical form as two great monuments of power, or Ancients. They have recruited Heroes from across the lands to fight their never-ending fued, dying amd respwaning in a constant series of 40 minute battles that bring the war no closer to an end. Stories are told of two great strategists of this war, by the names of Guinsoo and Pendragon, who realized the futility of the heroes' eternal defense of the ancients and set out to find a new way for the powerful entities to send teams of five powerul beings against each other. To this end they formed the League of Legends, which, as you state, intended to create peace. But the combined power of the champions only ignited more wars, and many flames were beheld. This is undoubtedly because those in the leagye have confined themselve to petty combats, ignoring the real issue at hand: the defense of the Dire and Radiant Ancients. These greater forces compel all to their cause, even those in the League. The Leagues' battles are but a cheap imitation of the real fued, so they can hope for no success.

See, you're almost asking 2 questions here so I'll try to answer you 2 ways.

1. Since it's inception, the idea that fighting battles instead of wars will only lead to a greater war in the future when the powers that be oughNoxuscoughcough get strong enough to overthrow the summoners that currently keep them in check. The general merits have been seen, as fewer people than ever are seeing ghoulish nightmares scouring the shadow isles, they're too busy feeding in the league which is allowing archeology and even tourism to the once abandoned land.

2. As for the success or lack there-of, I think it's generally agreed that Valoran has never been a safer place to live. That is to say, for the moment, until all of these battle-crazy, infinitely-respawning champions are allowed to leave the League.