In other parts of the World (eg Japan) any real universities are but copies of that Church generated-and-developed model.
In regions ruled by Muslims and governed under Sharia and the Koran there are few such schools and them under such ongoing attacks as ended Islam's "Golden Age" in Iberia and a few other places (C) by Islam's regression to its basic positions against such thinking as is beyond what is in the Koran, the Hadith (The collected sayings of Mohammed) and the writings of a few, very orthodox, Islamist jurists.
In the USA lower level schools were first established by Protestant religious groups and only later made public schools. Catholics, who did not approve of the very Protestant bias of those public schools formed up their own schools. They were followed by Jews and other Christians (And, others?). Those, largely New England, Protestants were the same or from the same roots as led the drive against the physical slavery of Blacks. [The ending of such slavery was accomplished only by force applied by governments (eg The armed acts of the US and Royal Navy and the bloodiest war every fought by the USA, being the "War Between The States") or by such individuals as Rev.. Henry Ward Beecher.
In many Muslim dominated nations the Islamists' bias against thinking-and-schools is matched by an approval and practice [ Even in the USA] of physical slavery as it is approved by the Koran and other teachings of Islam ].
I cannot but wonder if the well-reported failings our Universities and other schools is a result of a falling away from those Christian principles of intense-logic, in-public debate and "thinking" as so well demonstrated by the early Christian-Catholic universities and carried over to the early public-and-private schools of our Republic. [Catholics should specially consider that the shrinking of their schools seems to be concurrent with, if not caused by, their falling away from that inheritance and from orthodoxy. [The morphing of once "Catholic" universities to basically secular, sometimes anti-Catholic, schools appears to be the result of the same offense---Especially at "Jesuit" schools.]