Non-Burst Mages Will Never Feel Satisfactory To Play And Here is Why
The current game of League of Legends right now comes down to a few golden rules, being:
- There are no half-way builds, it's either full tank or full glass cannon. Anything in between will offer too little of durability or damage to compete with ever scaling damage of the enemy team carries or the ever growing brick walls of the enemy team tanks.
- Crowd control is completely useless unless it is either a.) CONSTANTLY applied/thrown out or b.) point and click or extremely hard to dodge. This is due to the excessive amount of cheap movement speed available in the game with 40% movement speed boosts being handed out like candy to everyone and then everyone who doesn't build movement speed has a dash. Everyone who doesn't fall into either of those categories is doomed to purgatory.
- The mid-game will never be a point in the game that decides a match. The early game will either decide it by having carries or tanks snowball ahead and win the "Arms Race" that is DPS vs Durability, or the game will stall out into late game, upon which the game is decided by how good the compositions are in team fighting and simply outputting raw, hard to hinder DPS.
- Shielding and healing champions are the only ways to reliably prevent death and be hard to kill if you aren't winning the "Arms Race". The less of these champions you have in your composition, the more perfect your team has to play or else you will be punished harshly for critical errors and mispositioning.
- Burst champions ALWAYS must be AHEAD in the "Arms Race" to function. Otherwise, the enemy will immediately be healed, dash away, shielded, etc. upon your rotation ending and nothing will have happened. This also means you have to be able to perform your burst unexpectedly, meaning you also have to be winning the "vision game" unless your champion has a way of getting around vision, such as some insane dash or invisibility.
Now, ask yourself, how does a Mage that doesn't almost instantly kill the enemy fit into these rules? Hint: Not very much.
lol
"not satisfying" 

. Burst is better against squishies and DoT is better against tanks. Aurelion Sol would be a way better pick against the team I listed than Veigar ever would be, no matter how much of an arms race either one has going for them.
Turrets for days. Only burst comes from ERW, which may nuke one enemy if all the rockets hit (otherwise, it is a meh MF ult).
Technically not a mage, but definitely builds AP and deals Magic DoT with poison trail.
Toxic Shot and Noxious Trap. More of Marksman Mage combo
Same with Arise! autos, though some burst with WQE Shuffle.