The first is perceived social legitimacy, which I don't think I need to elaborate much on: government recognition of a form of marriage implies formalized social approval of that type of relationship; "husband" and "wife" carry powerful private associations beyond "long-term girlfriend/boyfriend"; and in most modern societies the state's entangled enough with the institution of marriage that I'd expect a purely private claim to marriage status to feel like a cheat to many people.

Said social legitimacy is itself frequently also legally enforced, e.g., there having been cases of Catholic adoption agencies being shut down because they refuse to let gay couples adopt.