Sadly, I feel like a game type like this might be interesting for at most a game or two. League just isn't a game built around AI opponents.
And yes, I know that Doom Bots recently came out and was a lot of fun, but Doom Bots was exciting because Riot offset the poor strategy and decision making of bots with overwhelming power. This forced you to counter their massive power with smart play, hence the engagement.
But where champions have a set of abilities top play around (or in the case of doom bots, several sets of abilities), monsters just have base stats. When the only knob you can turn is base stats, you can either kill the monster or you can't, and I doubt that would make for a particularly engaging game.
Personally, I'd like to see a different take on the defend-against-waves sort of game. Have it be PvP, but instead of having champions fight each other, each team of champs would have to defend a "goal" line on their side of the map. Wave after wave of monsters of varying stats (slow but tanky, fast but weak, weak but numerous, or single fast and powerful monsters) would run passively across the map and try to cross the goal line, while the teams of champs would be trying to stop them.
If a monster crosses your line, your team loses points. The first team to lose all their points is defeated.
You could spice things up by having objectives on the map that can be captured to throw waves of monsters at the other team or give your allied monsters powerups.
You could add some tension to the gameplay by allowing players to spend the gold from their monster kills on either items OR upgrades for the monsters assaulting the other team.
You could open up the map to the players so that part of your team could go try to disrupt the enemy team's defense, but doing so would leave your own defenses weakened as well. Plenty of ways to add some depth and strategy while still having it remain fundamentally a monster-killing experience rather than a player-killing one.
Wait, scratch that idea. Not waves of monsters... waves of 
