High damage, high defense, and high healing is fine for a PVE game.
Edit: for any idiots thinking I'm talking about items, I specifically lay out the fact I'm talking about the class's KITS.
A class that has high damage, defense, and healing all on its own is perfectly okay in games that give you the option to chose between solo play and squads. Why? Because you're fighting AI-controlled enemies, not other people. So it doesn't matter if you have all those strengths. When you're in a party, the other players will only be glad to have you. When you're alone, you can take on hoards of enemies solo. There isn't anyone you're being unfair to.
Such a class does not work in a PVP game like this one. The "hoards of enemies" it takes to fight you are 2-3 other players from the enemies' 5-man team. It's unfair to the opposing team if 3 players are required to kill you, leaving only 2 others to fight your 4 teammates on another part of the map.
If you earned that strength through your skill and calls, then such a situation is fine. If you're 12-0 then it should by all means take 3 enemies to kill you. But a class designed to require a 3 on 1 even when they aren't doing great is not fine. Likewise, champions should not be able to go 12-0 simply due to large AD, HP, Armor, Low/No Mana Costs, and Healing advantages and easy-to-use abilities in the early game. Evidence you can find on any LoL stat site shows that despite easier abilities, these champions don't pay for it at ranks where higher-skillcap champions shine. They're just as strong, and in some cases stronger despite their easy nature.
Riot attempts to balance this with medium range and a "lack" of mobility. But Stormraider's Surge and Black Cleaver completely negate this weakness the moment you attack an enemy. And many ranged champions' max range is shorter than the CC range given to this class. So the supposed weaknesses are far too easy to overcome.
No other class in the game can so easily overcome its weaknesses. In fact, in the past items have been nerfed for being too good at covering their users' weaknesses. Rylai's was providing too much health, damage, and a slow to cover the class's generally squishy nature, and intended choice of Rylai's slow over more damage. Sated Devourer completely ruined the balance of 3-hit passives by making them 2-hit. Deathfire Grasp provided far too much extra damage to mages and AP assassins whether behind or ahead, covering their weakness to enemy heals and shields.
The class really shouldn't have innate sustain on top of both killing and staying power, but if that is to stay then Stormraider's and Cleaver's Rage passive need to be nerfed or removed.