Funny enough me being annoyed at how wrong the first paragraph is goes into why the second paragraph doesn't really mean anything for the education of the world as a whole.
The major religions of the world did not 'keep the world ignorant', in fact within their ranks, be it the Catholic church, the Islamic empire, or the assorted Asian cultures that all had different degrees of spirituality, all were the vanguards of scientific progress.
Understandably I can agree with you on the transportation of knowledge and lack of free time. But there's plenty of instances in European history where scientific advances were deemed heretical and those scientists were often forced (many times on promise of torture and death) to recant their theories and give up on their research.
I am not condemning religion I am simply looking at historical examples. And if you compare Medieval-1700 Europe to Eorzea there seems to be far less persecution of knowledge seekers.
And personally I feel that if the Umbral Eras can be stopped we'd see the Eorzean society advance faster than we saw our own. Especially since they have a genius like Cid leading the way.