Random ultimately ensures that alt-accounts get their mains while you get something you can't play.
League of Legends punishes people who don't min/max wherever they can and Random Select in various modes just drives it home. It doesn't stop overpowered Champions from entering the game. It simply prevents the other team from responding to it. One or more of the top tier Champions find their way into virtually every ARAM game, essentially assuring victory at the loading screen. With rerolls and trading, you can reliably get the same 1-3 Champions that you desire a very good amount of the time in Random modes.
Seriously, if people could just pick the broken Champions, it also allows the other team to anticipate it and formulate a team to deal with it, or just pick those Champions themselves which will result in a skill match-up. These are not ideal scenarios by any means, but each situation is better than what we currently have for two reasons:
- You can feel genuinely outplayed because you both had x broken Champ on your team; the outcome isn't preordained at the loading screen.
- You can at least lose with a Champion you enjoy playing.
Of course the cure-all to this is UNLOCK. THE. ROSTER. in Random Select modes.