Has the game gotten to a point where balance is impossible?

So i was thinking about this earlier today. More specifically what seems to be the biggest issues in the game. I basically came up with the answer that the game has gotten too large for balance to really exist any longer. We have champions with insane kits that barely need items to function, and champions that are so item dependent that they basically fall apart at the seams if they can't abuse them. Take for example a champion like , in a vacuum (no one gets items) this champion has all the tools to be oppressively strong built straight into her kit. Items means she can do her job better, but you don't need them to harness most of her power (yes i know the upgrades are big part of her power, but those could be changed slightly to trigger off other stuff like level / length of game / etc..). Then take for example a champion like , you have a kit that is by no means impressive in a vacuum, but can abuse items like / / or any other on hit type of effect. There is also the issue with champions that end up strong without having to really work for it. The enemy who went 2/10/x by the 30 min mark will still likely have enough sustain to shrug off 2 non-carries going ham WHILE ALSO having enough damage to be able to kill a squishy champion.

There is also the question of a champions strength in different levels of skill. If a champion DOMINATES the competitive scene but is garbage for your average solo Q player, do they need to be nerfed? What about the opposite, a champion that is face roll easy to win with for the average player but 1000% useless once you get into high elo.

Items are also a huge issue. How do you properly balance an item that is broken on one champion and garbage on another? At what point do you nerf an item versus nerf the champion who abuses it? Is broken because can abuse it? Is broken because she can trigger on her whole team? Is too strong because and can trigger it with a long range poke? Does function as a champion if he can't trigger on hit effects with his poke? Would anyone buy if it didn't have the double on-hit trigger passive? Is the item too powerful given the number of champions with very strong on-hit abilities as part of their kits, that would otherwise require a fair bit of set up to make use of. But the most important question is how do you really test the interaction of 150 items on 150 different champions, with the complexity of every champion using every item against every other champion? Now multiply that with 10 different champions all slamming into each other.