I agree that there should still be simple champions, but I stated that he could probably use a "soft rework". So think about it like the recent Garen rework. It kept all of his core mechanics but added a little bit to it while taking some parts out to make a more interesting champion that brings more to the game than the old Garen.
So with Amumu, his passive is kinda boring and I think it could be modified to benefit him more and help his jungling as the mr reduction does nothing for him here. Other things to consider would be additional effects to his E other than the reduction to basic attacks as again this is kinda bland. Something that would help him stick to a target might be a better tool for him. They really should reduce the hitbox of his Q and I am sorry, but it is way fatter than the animation and he should get the Leona treatment on this one, but if this hurts him too much, he can get buffs in the form of CD's, mana costs, and damage increases on abilities. If he were to receive such a rework, I think he would keep all of his abilities in their core function, but there would just be a little bit more to him.
I will admit, I haven't played the new Garen rework. I think it's pretty strong on paper, and I might enjoy him a little more thanks to his new "anti carry" role being emphasized, but Garen has historically been a boring champion for me so I put him on the list.
As far as Annie... F&#@ that champion. I don't really see why anyone would play her if she wasn't strong and the worst part is that she is incredibly strong and easy. Give that ult a cast time ffs Riot and maybe I wouldn't consider her such a dumb champion, but that's really what she is right now: dumb.
I do see the need for mechanically simple champions in league, but I also think they should bring something truly unique to the gameplay experience as well as having a more dynamic play pattern. With someone like Annie (particularly Mid/Top Annie), it is really just bursting out your opponent within the duration of your stun to take them out of the fight without a real chance for them to react. Annie's Tibbers is the ONLY ranged AOE instant cast Ultimate in the game and one of the only abilities in the game to have this uncounterability to it. Other instant cast abilities are single target or a zone effect like Malz or Soraka E (these might actually have cast times, I'm not sure).
I think that Riot can make these champions better is what I'm saying, even if their kits don't go through drastic changes. Annie can be a better champion and still be simple to play. So can Amumu and I think a soft rework could give him that.