It also shares aspects of the medieval college as a place of learning, & as you state, there is a distinct absence of 'religious' practice - of course the earliest Universities were often founded & run by Churchmen. However Rivendell has an aspect which neither Abbeys nor early Universities had - it was, as Tolkien stated, a
homely place. I'm sure (now you point it out) that Tolkien drew on the image/ideal of the Abbey, & as well as the University, but also on the Hotels & pensions he would have seen in Switzerland.
here
I think, as was usual with Tolkien, a lot of things went into creating the secondary world, & I don't doubt that the Abbey (at least its 'ideal' went into the mix)