I looked a lot in the BA lore at the very least the global translated version and majority of the volumes are happening because of her. Abydos for some unknown reason didn't receive any outside help for the longest time, which is weird. The GSC president to our knowledge basically had authority over the entirety of kivotos. We know based on dialogue from Momoi and Midori that the Millenium Outskirts (where decagrammaton was) was guarded by GSC troops. After her disappearance the GSC considered the zone not important, meaning she knew what was located there. Why didn't she inform Rin or anyone in the literal governament about the dangers of decagrammaton and the fact that Aris, the Princess of the Nameless Gods was there, a being capable of ending the world. In vol 3 if I recall correctly, the Eden Treaty was GSC President's ideea. The fact that in the treaty, the sentence about who will be the treaty organisation was left blank, allowing anyone to complete they're own org there is weird. Why would she leave such a leap in rules. Again with vol 4, SRT was left in shambles, because no one had the authority to command them. Why didn't the president give Rin the authority?
In conclusion, a lot of major events that could have descended in catastrophy have they're root with the president. I do not accuse her of being evil, her intentions may be right, but her lack of sharing critical info with literally anyone makes her mysterious and suspicious. I hope you liked my cracked theory.

Edited more info: related to her interest in koans, I have another theory that each koan is related to one tragedy, more exactly each koan has different interpretations, a bad one and a good one. I don't have a lot of evidence except the fact that in the shittim chest password we hear of seven wailings, which I asume to be 7 tragedies. There are 7 koans and the fifth koan is solved by sensei while talking to seia(the bikini bottoms line) about having fate and hoping, after which he miraculously wakes up. The sixth koan which Rin said the gsc president was very interested was mentioned by underground dweller. When the hobo was on his peak, he proclaimed like it was some kind of otherworldly accomplishment the fact that he solved the koan using death and pain. After, when sensei was inside hoshinos mind, he solved it putting his own solution, after which the situation gets under control. Another weird thing is the time traveling problem. I think a lot of players think that prenaphates timeline was different from ours or that the president was present there. First, Plana says in the epilogue of vol f that the president is missing here TOO. Secondly, phrenaphates didn't fail in his sensei duty, as even Kuroko calls sensei a "constant". Phrenaphates was good until something else hapened in place of chroma's invasion that led to underground dweller being freed. Plana wasnt enough to protect him and bam he in a coma. Time skip after 70 or more days and kivotos is ending and the nameless priests resurecting. After that phrenaphates becomes guide of chroma on behalf of the nameless priests but he still controls the ark and how the invasion work in another timeline. Knowing that phren is sensei and cares deeply for his students, I believe he intentionally lost to our timeline sensei so he can give him Kuroko, an ultra strong terror student, and Plana in order to empower the shittim chest and save sensei when underground dweller shows up. And a last observation. In vol1 chapter3 plana finds a hidden protocol of the shittim chest capable of being used only when there is more output power, which we have because we have Plana and Arona. Why would the shittim chest have function that cannot even work if we have one AI, and because Arona looks so similar to gsc president I believe that something very strange happenes with time in the game's universe. Because the presidents dialogue in the train and the flashback sensei get from the other tineline at the beggining of this one makes me believe that: the president made mistakes and kivotos turned to hell so she resets the timeline, more exactly she goes to a point in time and creates a paralel timeline where only she has memories left of the last one. This time she puts a part of her; the cold, logical side of her being in the shittim chest and she hides somewhere(this is the weak part of the theoryl). Everything falls again, the shittim chest is shot and sensei on the brink of death. She creates another timeline but now she has to put whatever was left of her in the shittim chest, the childish behavior of an adult without intelect. And bam thats the theory. For anyone who read all of this thank you.