It's an interesting idea, buit I don't think the POD workls. There is simply no central authority strong enough at the time to impose its will on the founders of omnasteries ("imposing your will" on people like St Martin of Tours or St Schenute is a losing proposition anyway). Perhaps instead you could have anchorite monasticism win out, with the church frowning on cenobites. That would remove most of the imeptus of monastery-founding because, what's the point? Real holy men go off and live alone as they have akways done. AS a tradition, it actually makes more sense.
Regarding the impact, it is liable to be the smaller the closer you get to the Mediterranean. Irish culture will be unrecognisably different, and Anglo-Saxon Christianity will also take a radically different form. THe antiquarian scholarship that fuelled the Carolingian Renaissance would not be available, creating a longer living tradition of Latin, but a gradual loss of the classical version (with a likely later rediscovery). The Christianisation of Germany proceeds more slowly and less thoroughly. Learning and tradition would find their homes in episcopal schools, which were much more rough-and-tumble than monastic ones, and ITTL would likely never close their doors to laypeople. It is quite possible that northern Europe will acquire something structured more like the early universities as its primary form of higher education in the 1000s.
THere would also be an enormous loss of manuscripts because episcopal schools had a much higher turnover. Monasteries would oftzen produce a book soli Deo gloria and then put it in a box and forget about it. Episcopal schools would of necessiuty be far more utilitarian.
Ii should also be interesting to consider a) what will come of Europeran agriculture without the monastic settlement movement and b) who ends up owning all the land that monasteries swallowed up IOTL. If it's the bishops, the church will be far more powerful politically and much less likely to obey a pope. And even if nomt, the papacy as we knopw it could well be DOA in this timeline. It lacks its best enforcers, the Anglo-Saxon monks trained in a school of unquestioning obedience.