New Game Style Suggestion

So we have ARAM URF and others which rarely show their head anymore, but I was thinking, why don't we introduce a game style where each player has a set number of lives. Whether it be 10, 15, 20. So when that play dies X amount of times, he is no longer able to respawn. This would really put more effort into risk vs reward style of play. Do I play safe and try to maintain lives to outlast the enemy team, or do I go for glory and try to disembowel the enemy team lives early at risk to my own.