AP Poppy is one of the worst assassin picks you could possibly make. Assassins like Akali and Katarina get cd resets for a reason. Their teamfight presence would be immeasurably lower without it. Once Poppy blows her burst, she's done, teamfight's down to a 4v4 and there's not really a whole lot you can do. The reason I compare her to Veigar, is because that's pretty much what he does too. He absolutely erases one target, and then would be useless, were it not for the fact a portion of his burst is AoE, and that ridiculous instant AoE stun. Another advantage Veigar or other assassin have over AP Poppy are decent AP ratios. She has an AMAZING 1.96 AP ratio before extra AP ratios like DFG and Lich Bane (Ok, I'll grant you she gets slightly more out of those than other champs because of her ult amplification, but still.) That's absolutely abysmal.
Let me say this again, so we're clear.
She doesn't even get 2 damage per point of AP. When she uses her ult. She gets more than that with AD burst (AA + Q).
Sorc Shoes are certainly a must on AP Poppy, because she already scales so little you don't want that scaling mitigated by the fact every single champ already gets 25% built in damage reduction to her.
Sorc Shoes are not a must by any stretch of the imagination on anything else because almost every other boot is so much more useful.
[/ap poppy hate]
Ok, now I've had my say and there's nothing data vampires can do to stop it. I can move on now.
Oh good lord, you just don't seem to understand. Poppy AP Assassin needs Lich Bane because then you get the freaking awesome 1:1 AP scaling ratio on your Q in addition to the 0.6 AP, also getting Sheen early is truly devastating for opponents as it gives you like +80 damage on your Q, and because Q (and E) is all magic damage then Sorc Shoes are a necessity. As you have pointed out every champion starts with mag res so a flat mag pen of 20 destroys their mag res which makes you deal oh so much more damage.
I can agree with you saying AP Poppy is like Veigar in that she can nuke anyone, the difference is the Poppy can do it through an enemy team and is less squishy. Unlike Akali and Katarina who need to get the kill for the CD refresh, Poppy has short CD on Q so if target is still alive after first initial burst she can still pull off another Q or two so Poppy can burst down the enemy tank (especially with DFG as well) or any other champion regardless of the location or whereabouts of any other champions.
Now even if you are going some pure AD Poppy build Sorc shoes can still be extremely powerful because if your opponent is stacking armour then doing an extra heavy magic damage punch can turn the tide in a fight, of course going pure AD Poppy is silly, you need that Trin Force to do a huge hits and once you have that you might as well get Malady to just destroy all opponents regardless of their late game MR.
Please try and understand that Sorc Boots can make Poppy do ~15% more damage with abilities, you might think 15% doesn't sound like a lot but it really is, Poppy Q regardless of her build can hit huge numbers but it is all magic damage so mag pen is an obvious choice, especially for Hybrid Poppy as you probably won't be getting a Void Staff, so Sorc Shoes + Malady pretty much erases any magic resistance.