Tanks are real cc threats that can greatly reduce your damage output, but not damage threats themselves. You need to kill them because otherwise you won't deal damage to their allies, not because they're threatening to kill you.
Assassins that can't assassinate from full health unless they're really ahead. The point of an assassin should be to reliably finish off a target than an ally poked down to 50-70%, not to get a 100-0 pick. At the same time these assassins need the tools to actually be able to finish off those targets and get out alive - not to be useless if the other team just groups. There should still be the ability to save a 50% Ally from the assassin, but it should require outplaying the assassin, not pressing a button.
ADCs that are actually punished for being the front line. There's too many comments that an ADC isn't out of position if their team is there to save them, but it's not healthy for a kog'maw to front line and deal high DPS to your back line without dying. Honestly I think the ADCs are fine as they are aside from general damage nerfs, it's the
Supports. They can't have so much power to save any Ally that screws up. Supports should be a set up player, like the playmaker in soccer who doesn't score the goals but has most of the team's possession and gets loads of assists. The support should be the one setting things up, placing a good fight, getting the engage or positioning, and then maybe dying as a result but setting up a won fight. Supports need to be proactive, not reactive. I don't want to see supports just following their carry around and putting shields/heals on them and cc/debuffs on anyone that tries to attack. Supports should be making things happen.
Mages are in a pretty good spot in my opinion. Small damage nerfs across the board would be all they need, but their general gameplay is pretty healthy.
Bruisers need survivability nerfs, by a little. With tank damage getting guttered in the first paragraph, you'd otherwise end up with bruisers just building full tank and doing damage to replace them. Reasons it shouldn't happen is that tanks will get most of their survivability out of their kit's cc and damage reduction that bruisers simply won't have access to, meaning they won't have huge survivability even if they build tanky. Their compensation is that they're still a damage threat though, at least if in range. A bruiser should win 1v1 if they get in range of any other class (but take too long to kill a tank with less damage than mages/ADCs, and have difficulty getting in melee range of mages/ADCs. Their role should be to draw pressure, either winning 1v1 and taking objectives, or forcing multiple enemies to stop them opening their team to get objectives.
Junglers need less agency, regardless of class. Aside from a few specialists who you know will try to early gank and will fall off if they don't get fed early, early ganks should not be a thing. Junglers should take significant damage during their first clears until they have good items built. Give early game / Laning phase bullies a chance to get a lead before junglers can interfere without taking a huge risk / sacrificing a lot if they don't get a kill.
I think I've covered roughly everything except unique Champion balance or playstyles (e.g. I don't want to get into resourceless sustain champs like Vlad).
In summary:
Tanks do very little damage, but their presence should open you up to damage and greatly reduce your team's damage output on their allies. You have to kill them because their team will kill you otherwise, not because they'll hurt you. Like a 70% damage nerfs with some survivability buffs.
Assassins shouldn't 100-0, but should be much better at finishing off kills that allies set up. Like a 40% damage nerfs on the ones that can 100-0, with mobility buffs.
ADCs and mages only really need a 15-20% damage nerfs on the high damage ones. No compensation buffs.
Supports need big nerfs /a full rework. Give them more proactivity. More ways to force favorable fights or to set up favorable defenses against a potential engage. Get rid of their ability to just cover for any allies mistakes.
Bruisers need slight damage/survivability nerfs in line with mages/ADCs (keep overall power similar).
Jungle influence should come in a bit later, unless you've clearly indicated otherwise by picking an early game specialist. If you're not on Shaco/Lee/etc... I shouldn't be too worried about a level 2/3 gank, and if you go for one anyways I should have the real threat to turn on you and get a kill back.
