It's rarely ever built full AP, and yeah, sometimes they just leave it on Executioner. If you really want AP, you should definitely buy Liandry as it synergizes well with her E, plus it's pretty cost effective overall. There's not much reason to force Rylai's like that. Luden's and Deathcap are both fine, for example.
The items you see being built on probuilds don't necessarily have to follow a certain logic - most of them are, in fact, random, and they themselves don't always know what would be the best possible item to purchase. Not to mention you'll often see high elo people doing really weird, questionable things and get away with it just fine - it's one's ability to make good use of it that matters. It's solo queue, after all, and that applies to all Elo brackets.
The items you see being built on probuilds don't necessarily have to follow a certain logic - most of them are, in fact, random, and they themselves don't always know what would be the best possible item to purchase. Not to mention you'll often see high elo people doing really weird, questionable things and get away with it just fine - it's one's ability to make good use of it that matters. It's solo queue, after all, and that applies to all Elo brackets.
Credits go to The_Nameless_Bard for the sig!
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IDK which build I should add to the OP though. It's kind of all over the place.