Oh hay -- this completely unfeasible idea again. Hey, since you clearly put a great deal of effort into this, how do you reconcile the all-too-possible scenario where Players DURP and HURP both random Sejuani in different games. Both Players DURP and HURP dodge. After the dodge-timer expires, both Players DURP and HURP queue up for ARAM and get matched with each other (it doesn't matter if they're on the same team or not). They're both going to be assigned Sejuani.
Yeah, that's right -- you can't. Because you haven't put any thought into this non-idea (but you're not alone -- nobody who posted this untenable non-suggestion in the old ARAM subforum put any effort into answering this question either). At best, all you have is "WELL, THE ODDS OF PLAYERS HURP AND DURP GETTING PUT INTO THE SAME GAME AFTER DODGING WITH THE SAME CHAMPION IS REALLY REALLY REALL LOW" -or-* "WELL RIOT CAN JUST ADJUST MATCH-MAKING TO NOT PAIR UP PLAYERS WHO QUEUE-DODGED WITH THE SAME CHAMPION"*. But neither of these are solutions that Riot will implement.
Of course, this could by hypothetically mitigated if Riot allowed the same champion on both teams again (which they won't do). But that doesn't provide a solution if three different players all random Aatrox, dodge, and then get matched with each other when they re-queue up. Statistically probable or not -- it's something that can happen, so there needs to be a solution. And the people suggesting this non-idea don't have a solution to the very real problem they don't even realize they're creating. Unintended consequences.