If there was Random draft, we'd have an Axe every game he was available, being a really annoying unstoppable pain bottom lane, if you didn't have an appropriate high damage ranged character specifically set on countering him. Like we wouldn't even reach level 2, he'd just sit behind our first tower and farm creep waves completely at level 1-6 taking nearly no damage while slaying anyone who got in melee range of him!
In other news, if Random draft was implemented, it may keep people from wanting to unlock champions when they could just play -RD tell level 30 with tons and tons of IP.