Well, those were just a couple of examples of champions that are centralizing, not meant to be specifically the only champions that are problematic and that I personally see more than some others in game. As far as not playing specific champions, not having them unlocked does the same thing for the vast majority of games you will play, even more than the increased reroll points and lower chance of rolling the champion you will gain from unlocking more.
There is a point to it. To say that these issues are not known is clearly untrue, most people who play ARAMs know that these things go on. It's not a matter of skill really. Having a Ziggs on the enemy team 7 games out of 10 puts you at a severe disadvantage. Dodging his bombs isn't the hardest thing in the world, no, but that's not the only problem to having him there. Never having creeps is a big problem, a ten second long set of mines spread across half the walkable terrain is a big problem. Having 2-3 ARAM accounts on each team increases the liklihood of having to deal with this sort of thing every game by a substantial amount. Can you still win? Yeah, sure. The problem is that it saps any amount of interest you have in the game. You might come out of it with a win, but you're not going to have any fun getting it. For me, the game isn't about a win or a loss. I will fight tooth and nail to win against any team with any champion I roll, but having to constantly deal with extremely long range AoE champions in every game where the premise is a random experience feels like an exploit in the system. I'm not suggesting that they should make every champion free for ARAMs, and in fact, acknowledged immediately that I know they will not do that. I'm saying that that is a possible solution, which it is. An increase to the total number of rerolls you can earn based on champion pool is an idea. Unfortunately, that would simply cause every player regardless of whether they have 1 champion or 100 to look for the same 10 or so champions, whether it be by only having the ones they want in the first place or rerolling until they get them. At the end of the day, the problem I have with the entire thing is that it just isn't in the spirit of the name. There is very little randomness in the process at this point because so many people intentionally try to remove it. If the game mode was more competitively oriented, I would understand this a whole lot more, but it kind of becomes people just being jerks to one another by trying to get the best possible rolls every time. I don't claim to have an end all solution, that's why I posted this here. There are steps that can be taken to mitigate this sort of thing, but there is enough traffic on these boards that I was hoping other people might include their ideas as to how to improve the game mode as a whole because it is, at its core, an extremely enjoyable thing.