Once upon a time, a late game Mage could expect to earn 700-900 AP at full build. Whilst this is still possible on some mages, it is not viable on many.
A lot of this has to do with Rabadon's Deathcap. It is the most expensive item in the game, it is extremely inefficient if it is rushed, and it requires you to sit on three components parts before you can afford the expensive combine cost.
Say you have a 3.5 AP ratio burst. This VERY high. Lux, for comparison, has 2.25.
With Luden's Echo, Morellonomicon, and Rabadon's Deathcap you would have 432 AP, and such burst would deal your base damage plus 1512, and then another 143 from Luden's Echo. This is a total of 1655 damage. If you throw in TLD, it's another 223 damage.
If you replace the Deathcap with Gunblade, you would have 280 AP, and your burst would deal base damage, plus 980, plus 128 damage from Luden's Echo, and then finally, another 250 + 84 damage. For a combined total of 1442. And again, add in TLD, for another 220 damage.
Do you see why people are building Gunblade?
That's with an insane /3.5/ AP ratio scaling, and Deathcap still barely beats Gunblade in terms of burst when the other items are the same.
Except Gunblade is cheaper, also grants sustain, AD to help your auto-attack trades and tower pushing, and has a much better build path.