I have seen this game going over 9, almost 10 years.
League of legends is unbalanced since the moment that there is no possible counterplay for any situation in the game.
A lot of people have complained that defense items are useless, which is partly true. Here is the following breakdown of League current unbalanced state.
I will go directly to the grain because this post is what is it about:
The amount of damage CC skills do. It's insane how you can get 5s cc locked but in top of that you have to heavily get a 50% of your hp with that spell if the enemy is ahead. CC should be really punishing in itself, and damage sources should come for riskier spells to play.
Tank items overlap core items (bami's cinder with jungler item won't allow you most of the times to build sunfire cape as a jungler, etc). Another example is Randuin's Omen with Thornmail, it's just a disaster of all tanks build path. You have to choose between Crit resist, Grievous wounds, that's horrible with so many Yasuos in the game.
Darius can have only defensive items, and still output damage enough to do pentakills and outstand in the damage graphs along the game (same happens for nasus).
Master Yi Guinsoo combined with healing is nearly impossible to outplay, no matter the armor you have, the mr you have, or health, he will just blast you. He can even build Guinsoo into ASPD jungler item, then go full tank and shred all your team.
True damage in general, has no counter, which means that to win in the game, true damage is a safe bet (see cho'ga'th R, Vayne W, etc).
Champions like Fizz, Leblanc, Kassadin, highly mobile, massive damage, can pickpocket any marksman in a combo and get away most of the times without being punished if they are minimally ahead.
Impossible to tank unless you are Tahm Kench with Gargoyle Stoneplate or Nunu in steroids.
40% CDR is too easy to build. Jungler item = 20% CDR, so in most cases you can see Lee Sin with 45% CDR that is dope blasting everyone.
Jungle Role is depressing this season, and the impossibility to tank makes it even worse. I had 3 losing lanes in almost more than 60% of my games.
Flat % Health damage (Liandry's, etc) > another reason that tanks don't exist in current meta, they just get melted with such items.
Akali, Evelynn, and twitch > Vision in general needs a rework, true sight and true stealth is ridiculous as it sounds and vision itself makes sense but plat+ elo games become a vision rush fiesta.
If you find more reasons I will be working on this post, but for now I think fixing the ones above would be a really healthy starting point.