It would make perfect sense for there to be an aetheryte at the Gubal Library.
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Haha, yeah, you're right!
As for how Ala Mhigo ended up with such architectural wonders, there was an old bit of 1.0 lore that stated that Ala Mhigo was "the most technologically advanced of the six Eorzean citystates", yes, even more advanced than New Sharlayan, and with a ready supply of high quality stone at hand... Desperation also would have played a part, with Gyr Abania being so arid and the area around Loch Seld especially being so downright inhospitable, you'd want your new home to be able to withstand the harsh environment (being built right on top of an earlier city also helped too).
But yeah... something something "we have resources"....