The problem was that the Covenant never truly integrated. It was always a confederation of species, and besides intermarriage being biologically out of the question, the Covenant never encouraged *any* cross-species ties. The Covenant were cohered by the carrot of divine transcendence and the stick of planetary annihilation if you stepped out of line. Otherwise, Grunts did their Grunty things, Jackals did their space privateering, Elites pretended they were better than everyone else and the Prophets schemed. It's highlighted in the books when a character actually had substantial relationships with another species (the Prophet in Broken Circle, Regret in Contact Harvest, etc.)