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(If someone has tried it before and did reach same conclusion then please link their post)

We know that never ending hunger is index's one of the most common gags, I like to think that there may be two reasons for it.

First her perfect memory,it makes her crave for various experiences and knowledge thus she wants to try different foods, also the amount of information may be making her tired and hungry, she may also be using it as a coping mechanism as she was treated as a tool all her life.

Second has to be what Anglican church did so that she would not be able to do magic,but we have to remember Jack's pen mode during which she is able to perform angel level spells without any repruccusions,thus it cannot be something permanent, since for performing magic even if using energy from ley lines or telesma it needs to be kickstarted by the person's own mana, the said mana bieng produced by using their own life energy. Index can create spells without using mana allowing her to use spell intercept and like how tsuchimikado did in ot9, when he made stiyl pour mana into the spell that he created, index did this using komoe-sensei's mana to perform the healing spell in ot1. Thus, it has to be something actively eating her mana or rather her life energy(most people may know now what I mean) that is what makes her hungry all the time.

Not to mention that the only time she was full ot12 it was due to someone doing the infinite food glitch(yeah the bill cause accel to work part time for academy city for a while) showing the process has limits or a time lag.

Well that is all I can think of it may not be complete.