This is the problem with turning a video game into a "competitive sport". These arguments really shouldn't even be happening for various reasons. These characters are there to add diversity to gameplay.
Ultimately what the competitive side wants is no diversity. If you compare it to a true life sport, all sports start with exact even teams. The only difference is the people playing (or in our case Humans).You can't have complete balanced gameplay the way LoL is set up. It just CANNOT happen. Certain characters are counters to others, while others are simply based on themes or to expand gameplay options. The only way a true balanced team would occur is if they eliminate the random first pick and banning, and require both teams to be the same characters.
By following the top 2% of players, you will eventually eliminate any diversity and fun in the game, because if they get rid of stealth (there is no way to fix it, face it), you also will need to get rid of tanks, because they are looked at in the same way. Then get rid of all global ults because it's just too unfair to the team w/o global ults. Then you need to get rid of the bursty ranged, because they are too OP for melee characters who need to get close, etc etc. Eventually all you will have is tanky dps (that's the way it's going already).
My suggestion. Leave it alone. It's not broke in such a manner that it isn't fun. Some people forget that first and formost it's a game. They won't though, and eventually will ruin it.
If you want to change it then make it simple. Characters that are 1 class rather than split classes:
Tank - NO DPS(none of this both crap) They do only 1 thing and one thing well. Tank. They have stuns, snares, slows, taunts, whatever, but do no damage.
DPS - They are not tanky. They do damage. ONLY. No slows, stuns etc.
Ranged (DPS or Mage) They do damage. ONLY. No slows, stuns etc.
Support - (NO DPS..stealth char could go here). This is only heals, armor, buffs of that nature.
Mages - They do damage. ONLY. No slows, stuns etc.
Of all complaints here are mine:
*Too many self healing characters.
*Too many tanks that dish out way too much dps (or vice versa)
But in the end, it's about having fun and diversity. Everyone is going to complain about one type of char being OP especially if that character directly counters the character they like to play most.