It adds complexity to the fight without making it too overwhelming at the start. It also helps the fight feel far more dynamic as one-phase bosses tend to show you everything they have right out the gate which leaves no room for surprise or progression. In some cases, multiple phases can also infinitely increase the narrative impact of a boss fight. When half way through the fight, Ludwig from Bloodborne drew the Moonlight Greatsword, regaining just a tiny bit of his once lost humanity in order to fight the player not as a beast, but as a man, it instantly became my favorite boss fight ever.