While many people have agreed that seeing the same champions over and over and over again can get stale, a very wild randomizer like this or simply adding more and more bans isn't an answer.
My idea first won't work in NA unless they drop the stupid one game format again and return to best of 3 series.
The best way to incentivize champion variety is to drop the stark W-L standings and shift to a point based system. Wins would of course gain points. Points could also be granted for major objectives like Herald, Dragons, Baron, and Inhibitors so even a losing team can walk away with a few in a game.
With such a system, points could be forfeited if a team selects a champion they used in a prior game.
Say for example downing the Nexus (winning) earns 5. Let's say every other major objective (Dragons, Herald, Baron, Inhibitor) is worth one point. A winning team likely will down a couple inhibs, dragons, and probably Baron. So if the game runs smooth and quick they net another 5 for a total of 10 in their win.
So, to discourage teams from only taking the same comps over and over in a series, a 3 point penalty per champ would do a lot to force teams to really think hard about cheesing the same champs every game while giving a little freedom to repeat using a comfort pick or two and have a net gain over a winning series.