Is gated in the early game because she is one of the strongest lategame champions in the game. Even then a skilled enough player can easily manage her early game and still get kills.
I've never heard of people complaining about his mana. 60 mana is hardly bad. And maxes out at 80. Problem champions have 100+ at max rank. Athene is even almost core on him because of the MR->AP making it better than Morello in almost every situation(mainly as long as he's not starved for gold).
His E clearing a full wave restores 100-130% of it's mana cost. This can chain into the enemy champion for easy damage. His Q and W are to offset this. His W isn't something you should be casting too often anyway. Q also has some high base damage, A 3 second silence(I think it's the last remaining 3s CC non-ulti in the game and it can hit multiple targets). Malz only runs into mana issues if he can't fully use his E. Which is easy to use with AA's and his passive helping. You just have to be smart about not pushing the lane and getting ganked.
Malz is the only pure mage of those 3.
Anivia is partly a support. If it wasn't for her mana costs she probably would be a top-tier support.
Galio is a tank as a primary roll. He just happens to also be able to get high damage while being tanky. Similar to Rammus.