Problem isn't with champion balance(as much), but with how Riot deals with champion balance. Just as an example Janna's movement speed passive used to be global, but they decided that global abilities just weren't fun (even though the only straight up OP global was Twisted Fate's original skill build). So they nerfed that to a higher move speed bonus in a small radius around her. In order to counter the lack of global power that people had high level and pro players decided to take early advantages by pushing towers in their carry lane with a jungler really quickly. Riot "balanced" these sort of plays by giving towers higher armor prior to 10 minutes.
Riot have a really shitty way with dealing with tactics, since they don't want games to be decided within the first 5-10 minutes. But then we reach the problem that they don't want games to be decided in the late game as well. It used to be for every inhibitor you took out not only would your creeps in that lane get more powerful, but your other lane creeps would get bonus stats as well. They just removed this because they felt that it was unfair on on losing teams (who in most cases deserve to be losing).
As it stands with champion balance it's the same as it's always been, someone get's powerful (recent examples being Kassadin and Lee Sin) and they nerf them as opposed to buffing other people to be able to compete. If everyone was unlocked on each account this would be fine, but they aren't. Hypothetically say someone buys Darius. He's pretty strong but nobody really pays attention to him because of the tank with 1 damage item meta that's going on at the moment. This person discovers that for some reason Darius wrecks Shyvana in top, he plays her, gets Diamond 1 or even Challanger, pro players and other top tier players notice and start playing Darius as well. Darius ends up being picked in LCS, causing scrubs such as myself to go out and buy him. 1 month later Darius is nerfed into the ground and you can't pick him again without being reported. This is what's happening with Kassadin and Lee Sin right now, although Kassadin in widely considered to be too powerful Lee Sin is agreed to be one of the most balanced champions in the game, but due to their popularity they're getting nerfed. It's a vicious circle that's not going to change until the balance team can do their fucking job right.
