This is a very scriptural view:
18 For, in the first place, when you assemble as a church, I hear that there are divisions among you; and I partly believe it, 19 for there must be factions among you in order that those who are genuine among you may be recognized. I Cor 11
So, how would those who are genuine be recognized? The Apostles and their successors the Bishops were centered around the authentic Eucharist. We know by reading the Fathers that the authentic Church founded by Christ is that which is centered around the Bishop and the valid Eucharist in his care.
You are right that a greater good will arise from divisions.