Interesting post, Hell West & Crooked. But not terribly accurate.
First, St Patrick's was a guest in the CAS competition from, I think, 1978 to 1983. It won no "unofficial" 1st XV premierships in that period, although its teams were certainly very competitive. It is simply wrong that "to remind them they were 'guests' these Premierships were never officially recognised." First, they won none - and secondly, nobody's premierships were recognised in this period. Not Knox, nor Barker, nor Trinity, no-one. "Official" CAS premierships were discontinued in 1941 and not revived until (I think) 1988.
What did happen was that St Pat's caused an element of confusion as to who the Premiers were, because some schools counted the St Pat's game in the "unofficial" tally and others did not. Thus in 1979, if I remember correctly, both Waverley and St Aloysius claimd the premiership on the basis that St Pat's beat (otherwise undefeated) Waverley and lost to St Aloysius (whom Waverley beat). But St Pat's (who lost to Trinity) were not in the hunt on any count. In 1980, Trinity claimed the "unofficial" premiership by omitting its loss to St Pats.
You may or may not be right about Knox - I don't know. And I don't doubt that sectarianism may have been a factor. But you've left out the most important point, which is St Pius. St Pats was invited to compete as a guest along with St Pius. No-one wanted to add just one more school, because that would have created a bye, which wasn't desirable. St Pius did not distinguish itself. Its rugby teams were not very competitive, but did attract a reputation for dirty play, while it had little ability to field teams in other sports (St Pats fielded cricket teams for instance - St Pius did not). So in the end what really killed St Pats chances of joining was the fact that they were yoked to St Pius, who did not come up to the mark.