Personal opinion of a silver player on how the classes should be
ADCs - not necessarily range. They should be fast but frail champions that can kite and deal increasingly more damage based on how long they auto/stay in fight and are always single target. Current in-game archetype: Vayne
Assasins - The most mobile class. The difference from ADCs is that they have skillshot bursts damage. Current in-game archetype: Zed
Mages - immobile, AOE/single target magic damage, but low range and little to no CC. You get too close to them, as a squishy, you're toast. You cluster too much against them, you're toast. Current in-game archetype: Brand
Utility Mages - they bring in the CC or the buffs. But they carry little damage. Should have a balanced kit, not overloaded with the same utility type (Janna:heal+shield). Current in-game archetype: Bard
Fighter: Balanced class. Their strength should be in flexibility. You want a squishier mobile damage dealer, buy those items. You want a tankier protector, buy those items. Their role should be disrupting the enemy team-comp and adapting to counter their style. It's the class that should need brains not only mechanics. Current in-game archetype: Jayce
Protector/Tank: They are immobile, but they ca soak in the damage. They should have only low range CC, little mobility spells and their kit to be designed to be able to handle burst damage. Current in-game archetype: Rammus/Braum
So what's missing? What's different. Well for starters, juggernauts. They make the game so hard to balance and so unfun. Let's take Trynda or Diana. Their kit is all in. While fighters, they offer little flexibility and their built paths are 90% of the cases the same: is all about bursting and surviving the burst. They're not healthy or fun to play against or with.
Why I started with that example? Well, because imho they are the cause to all of this imbalance. Hear me out: because of them, adcs need to burst. They always needed to be reflex-wise faster and do burst damage, else they ADC class will fall behind. It was never the assassin who was the problem, but the champion that will erase the whole team when fed. Keeping the ADCs bursty meant this class was never a top competitive option, but lowering ADC potential, here come the juggernauts to take the podium.
Here a simple logic "chart": Low ADC potential means assassins are not important. You lose two classes. That leaves in the current concept tanks, mages and juggernauts, or more precise: tanks that play like juggernauts, which because of their concept will always trump the other classes too and we'll return to the place where the game was a few years ago.
Getting rid and tweaking the juggernaut class means ADCs can be in line with what I said earlier: no burst damage, but incremental. Critical could be changed in a mechanic that each damage against the same target increases the damaged dealt by x% ammount up the critical cap.
Another problem is the sup/tanks item/kit overload: you'll get so much heal, shields or protect on the ADC
So this are my thoughts on the game balance