Melee overpowered compared to magic? Well, not in my opinion.
For healing? Nope, Cure Wounds is a good single nuke heal, but it has a lengthy cooldown. Water heals beat the pants off it.
AoE damage? Oh please, you mention one of the only AoE spells I never even had on my quickbar. Mages have Small Fireball, Chain Lightning, Acid Breath, Winter Blast, Infectious Flame, Earthquake, Storm, Meteor Shower, Hail Attack, Boulder Bash, Deadly Spores, Lightning Strike and Explode. Most of those can be done from up to 17 metres away, not much worry about damaging allies from there. Cooldowns? Who cares, I have a different spell to throw from the ridiculously large pool of available abilities.
Single target damage? Here you almost certainly are right, a warrior or rogue can lay on a huge amount of pain to one enemy. However this is not to say wizards are lacking, they can put out a lot of pain from long range, inflicting debuffs without compromising their damage in the slightest.
Buffing. The best buffs either come from talents or from mages. Oath of Desecration, Absorb the Elements, various elemental shield spells, Wildfire.
Crowd control. Nope, melee loses here again. Ice spells all freeze, air spells almost all stun (and the one that doesn't can throw an enemy 15 metres away anyway), some earth spells knockdown. That and a mage can easily summon creatures and create terrain effects to control the battlefield.
Having said all that, I don't see the melee as underpowered at all, but trying to say it's overpowered relative to magic is burying your head in the sand.
