You got me to do it... posting the numbers I ran on late game AP damage in comparison to (now old) Ryze. I've said before that Ryze falls off late game compared to other APs, so I ran calcs for just the beginning of late game (Which I view as the time where core builds are complete, which is about 10k gold for most every AP give or take 100 gold in some cases). I went with a 10 second time frame to give Ryze a fair shake since he's not bursty like most AP's and he can get off his full combo and then some. I gave everyone Blue Buff, since AP's get Blue Buff (Even gave Vlad Blue Buff, cry about it if you want to).
First off, here's a Ryze with a Tear of the Goddess (Fully Stacked), Mercury Treads, Banshee's Veil, Frozen Heart and Will of the Ancients will have 433 damage on his Q, 395.3 damage on his W, and 130 damage on each bounce of his E. His combo gets 8 Q's, 3 W's and 2 E's off in ten seconds.
So it comes out like this:
Ryze (Tear, Mercury Treads, Banshee's, Frozen, WotA):
x8 Q's (433) = 3463
x3 W's (396.3) = 1186
x2 E's (130 * 3) = 780
Total Possible Damage:
3463 + 1186 + 780 = 5869
Next I did the numbers on Anivia.
Anivia (Archangel's Staff (Fully stacked), Sorcerer's Shoes/any boots, Rabadon's Death Cap, Void Staff) (Total AP 480)
x2 Q's (840) = 1680
x3 E's (830) = 2490
R 280 Damage per Tick
Total Possible Damage:
1680 + 2490 + 2800 = 6970
From Q and E alone you're getting 4170 and to start doing more damage then Ryze at the same point in the game one would need to stand in Anivia's ult for 6 seconds. You may scoff at this but when she get two stuns off and can wall your escape, you stand in it for quite a while
Ahri (Rod of Ages, Boots of Lucidity, Rabadons, Void Staff) (Total AP 448)
x3 Q's (576) = 1727
x4 W's (660) = 2640
x2 E's (337) = 674
x3 R's (314) = 942
Total Possible Damage:
1727 + 2640 + 674 + 942 = 5983
Ahri does more Damage than Ryze even at 0 MR, let alone that 863.5 of her damage is True, and the fact that she is the most Mobile AP in the game making her very powerful late game. However, the argument can be made that her damage is skillshots/non-targetable, and those can be dodged/miss whereas Ryze's are all targets. Either, way, I'm not going to get in an argument that one champs late game is inherently better because they're easier to use, just that his late game isn't his strongest point, so you can take these numbers or leave them.
Swain (Rod of Ages, Sorcerer's Shoes, Rabadon's, WotA) (Total AP 462)
x2 Q's (E empowered) (805) = 1610
x2 W's (E Empowered) (676) = 1352
x2 E's (Empowered by itself... it's weird) (725) = 1451
x7 R's (E Empowered) (219) = 1533
x3 R's (182) = 546
Total Possible Damage:
1610 + 1352 + 1451 + 1533 + 546 = 6492
So here we have a champion who has strong Team Fight Sustain like Ryze late game, and is dealing MUCH more Damage in actual team fights. For example, this is Swain's Total Possible Single Target Damage. If there were three targets around him his ult would be dealing an extra 3640 total damage in the fight, all while healing him for 30% of the damage dealt.
This is why I found the comments that "Swain has no late game" rather hilarious, because he has one of the single most powerful late games in the game, not only by virtue of raw damage, but also by virtue of team fight sustain.
Vladimir (WotA, Sorc Shoes, Hextech Reveolver, Rabadon's, Void Staff) (Total AP 485)
x2 Q (521) = 1042
x2 Q (R Empowered) = 1167
x1 W (R Empowered) = 503
x1 E (No Stacks) = 398
x1 E (1 Stack) = 443
x1 E (2 Stacks R Empowered) = 547
x1 E (3 Stacks R Empowered) = 597
x1 R = 690
Total Possible Damage:
1042 + 1167 + 503 + 398 + 443 + 547 + 597 + 690 = 5387
Yeah. I wasn't expecting this one either. Core Build complete and he's not doing that much damage (Less then Annie in the same time frame). His main virtue lies in his sustain and natural tankiness from the passive. Also, I have a feeling that a 6 item Vlad will start being more on par with everyone else, but didn't run the calcs. Still, I like his late game more than Ryze, because that ult Increases EVERYONE's damage by 12% which is more powerful (in my personal onion) than Ryze's 50 extra DPS and extra tankiness. You can say it's not as effective if you want, I won't argue.
Cassiopeia (WotA, Boots, Rabadon's, Rylai's)
x4 Q's (627) = 2508
x10 W Ticks (130) = 1302
x20 E's (429) = 8574
x1 R = 710
Total Possible Damage:
2508 + 1302 + 8574 + 710 = 13094
Yeah. While not nearly as Tanky as Ryze is late game, she's more than twice his Damage Potential. And if you keep the minimal amount of poisons on for ten seconds to keep the E cooldown low, she's STILL twice Ryze's Damage Potential. Not to mention AoE CC ult utility for team fights. Definitely a stronger late game.
Karthus (Rod of Ages, Boots, Rabadon's, Void Staff)
x13 Q (509) = 6614
x10 Ticks E (222) = 2220
Total Possible Single Target Damage:
6614 + 2220 = 8834
Total Possible AoE Damage:
(254 * targets hit) * 9 + (Total Ticks on all targets * 222) + (818 * 5) = A lot. Too many arbitrary variables but you get the idea.
Karthus has no need to be super tanky or sustainy since his entire purpose is to die in the middle of a fight and deal tons of AoE damage and fire his ult off to deal 4090 damage to an entire team, plus the damage he deals before he dies in the fight, and the damage his E deals while dead. Just overall a better late game then Ryze since he naturally has shorter cooldowns better AoE and doesn't have to.
Kog Maw (Archangel's (Fully Stacked), boots, Rabadon's, Void Staff) (Total AP 472)
x2 Q's (590) = 1180
x2 E's (590) = 1180
x13 R's (542) = 7041
Total Possible Damage:
1180 + 1180 + 7041 = 9301
AP Kog here showing how powerful he is by dealing more damage than many of the current AP carries with his ult alone at a considerable distance, which mitigates how squishy he is. This calculation also does not mention the 10% of your max health his 710 range Auto Attacks are dealing, and with the passive Attack Speed buff on his Q, he hits you around 12 times (if I calculate AS per level scaling correctly). Powerful pre-fight Poke Damage, a ton of DPS in team fights all while staying relatively safe.
Veigar (DFG, Boots, Rabadon's, Void Staff + 75 Q Farms) (Total AP 536)
x5 Q's (582) = 2910
x2 W's (856) = 1712
R = 1143
Total Possible Damage
2910 + 1712 + 1143 = 5765 + 47.5% of one target's current health
King of Single Target Burst, and he scales into late game infinitely with that Q. You'd actually probably have more than 75 Q farms for champ kills and if you dedicated mid game to farming it. AoE Stun and the ability to completely kill one member of your team in a full combo. Not to mention that I didn't even factor in if Veigar used his ult on an AP champion. I like his late game more than Ryze, but you can go ahead and dislike him if you want. It's not a big deal to me.
Kennen (WotA, Boots, Rabadon's, Zhonya's) (Total AP 462)
x4 Q's (582) = 2326
x3 W's (439) = 1317
x3 E's (522) = 1566
Max Ult per Target = 1184
Total Possible Damage
2326 + 1317 + 1566 + 1184 = 6393
Kennen does straight up more damage for an Armor and MR buff that put his defensive stats on par with Ryze (that has a downtime of half a second when armed with Blue Buff) while also having a 2 second stasis. Further, he has more utility and mobility with his Passive Stun and E.
So these are all mage champions that are popular that have better late games than Ryze (Albeit Swain and Vlad go top Lane)
Another reason why Ryze is not as powerful in comparison to other Late Game AP carries, is because the only damage multiplication he gets has already been applied at this point in the game, with his max CDR. He can get a Void Staff and deal more damage, but that's money not being spent on tankiness, for an item that is simply more effective on AP Champions than it is on Ryze. Not to mention, that some AP's already have it and are doing more damage than him regardless, so he'd only buying it would only be an attempt to catch up. Further, the AP carries can increase their possible damage even further by getting a CDR item like Morello's Evil Tome, or Deathfire Grasp late game, which would increase their over time DPS even further, while ALSO dealing more straight up burst damage.
If you want to argue that it's his tankiness that makes him powerful late game, then let's take a look. Ryze's "Tankiness" totals to 2283 HP 180 Armor and 105 MR. As far as tankiness goes, that's rather weak. The only thing that keeps him alive long enough for you to think he's really tanky is the Spell Vamp ultimate + WotA, which is interestingm since that's exactly what some people last night on IRC were calling a passive spell that didn't feel like it does much beyond continue his combo. Vlad, Kennen and Swain all get similarly tanky while in the case of the latter two, do much more damage. Anyways, if you really wanted to make him more of a true tank, you'd build something like a 6th item Warmog's or even a Rylai's, but again, these item buys on Ryze don't add anything to his damage, which will make his late game damage fall off harder in comparison to simply be tankier. This may seem like a benefit to you, but it means he can't invest in MPen which means a single MR item makes his damage fall off even harder, making him less of an overall threat.
TL;DR Maths. (Old) Ryze's late game fell off. His utility is lower than other Mages, does less damage, and in certain cases is not even that significantly stronger in terms of tankiness.