You will note that MMA is dominated by non-Eastern practitioners. The Greeks gave us western wrestling which is a large component of the successful grappling ground game.
Excepting the Orthodox factions today, there is no muscular Christianity in the West; all the Protestant and Catholic factions have been in a race to feminize their congregations to the point of the weak-kneed and morally anemic flaggots that people the American churches from sea to shining sea. They fly national flags in their worship halls and the prevailing government supremacist interpretation of Romans 13 is illustrated no better than the prostrating positions and keening wail of obeisance during the house arrest of the Peking Pox.
Starting in the eleventh century the Crusades began against the Muslim foe for hundreds of years; this set the tome for the creation of martial chapter-houses, brotherhoods and the knight ideologies that created the notion of bladed training salons where adherents refined the martial arts of the west to a very high degree. There are probably hundreds of training manuals in Latin and German yet translated from those eras. Before the advent of firearms in the common use, the blade was the choice in close combat and private instructors were abundant. monastic orders literally provided warrior muscle for the Crusades.