Mages and Balance
Since the early days, Riot has changed League of Legends much. So much so that there isn't much of a reason to balance mages by cooldowns and mana costs alone anymore.
In the past, cooldowns and mana costs ensured that the entire class of mages, who then had a lot of reliable point-and-click damage, wouldn't be overpowered compared to the rest of the champion pool.
Now mages are balanced because most of their abilities are extremely dodgeable. Today, many mages are slightly weak in the early game against high DPS champions. Well-played marksmen can push most any champion out of lane, and mages are no exception. Tankier targets who can survive a mage's initial burst also present problems.
In no special order whatsoever, here are mages I believe could use some buffs which would not make them overpowered by any means.
Anivia - R width, R leash range. -Makes Anivia a better Area of Denial mage.
Malzahar - W reliability, R damage. -W is extremely useless. R base damage is very low for a channeled ability.
Azir - Q cooldown. -Soldiers are too immobile.
Lux - E width, R width. -Abilities are too easy to dodge for their mana and cooldown cost.
Brand - Passive scaling. -Not enough scaling with deathcap.
Karthus - R damage. -Iconic ultimate has barely any damage.
Kennen - W damage. -Kennen's waveclear is low compared to other mages.
Morgana - R 2nd activation scaling. -For an ultimate that places Morgana into grave danger there isn't a high enough reward mid and lategame.
Nidalee - Q width. -To bring back old Nidalee poke-siege comps. Even Faker misses this.
Veigar - E activation delay. -Delay is extremely long.
Vel'Koz - E activation delay. -Delay is long.
Xerath - Q width. -Q is too easy to dodge.
Zyra - Q base damage. -Q base damage is too low.
None of these buffs would make the mages overpowered, but they would be much more satisfying to play.


