Monastic Domination of the Catholic Church

I've been thinking about how at certain times and places in history the Catholic Church was dominated by monks, as in the early Christian Community in Ireland, which from what I understand was organised around monastic communities, the Monastic State of the Teutonic Knights, and those Abbey which grew large and powerful enough to become great centres of learning and wealth, like at Cluny. Further, many monks and abbots have reached positions of high standing within the larger Church, as exemplified by the Cardinal-Abbots, but in general have played second fiddle to the clergy who start out as parish priests.

So, how might monasticism in the Western/Catholic Church come to dominate the Church hierarchy, to the point that abbots have an equal if not greater number of cardinals than the regular archbishops, and are responsible for tending to the spiritual needs of large swathes of the lay population of Western Europe. Further, what effect might this have on the theological development of the Church?

As a bit of extra fun, what do you guys think of a system of territorial abbeys replacing feudalism in certain regions, abbots taking the place of counts, and positions like the benedictine abbot-primate replacing higher titles like duke?
 
The simplest way to have a monk-dominated Roman Catholic church is to institute a reform allowing married priests - at the parish level but not above, as in the Orthodox churches. Thus there is no line of promotion for ordinary married priests, and all the hierarchy, from bishops upwards, is dominated by candidates drawn from the monasteries, since monks still take vows of celibacy. This as I understand it is the position in the Orthodox Churches today.
 
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