PvP in PvP possible transition

At the end of the Phoenix vs Phoenix in Protoss vs Protoss daily, my mind had to ask the question as to why a protoss player shouldn't transition into carrier to counter phoenix. We already have a fleet beacon for the anion-pulse crystals, and are likely to have started air upgrades. The carrier is a non-light unit that has base 2 armor so will recieve very little damage (3x2 unupgraded) from a phoenix. As day[9] argued our opponent should not have many stalkers since we could have killed him off with our phoenix.