I never heard of this practice until two years ago, and I have of LOTS of broken engagements.
GAW. what you said makes a great deal of sense. Of course if one contemplates getting engaged, breaking it off, or getting divorced, advice should be sought from people who can help the person. That is NOT the same as saying one should ask a shailah. Shailahs are specific halachic questions. They require a p’sak, not simply advice.
I guess I take issue with the notion that every single aspect of one’s life needs to be addressed to a rov and governed by his pronouncements. We need to be adults and take responsibility for our own decisions in life, as well as charge of our lives. If I splashed a drop of milk in the chicken soup, I have a chiyuv to run to the rov with the shailah. But – if I am thinking of moving into a new home, that is my business and doesn’t require the input of a rov, unless he happens to be my father/father-in-law, or a realtor. In my experience many rabbanim, contrary to popular belief, are NOT qualified by mere virtue of having semicha, to discuss personal issues and give helpful advice. An engagement is not a pot of soup.