That's how it works when you sing! But if you have an instrument you need to tune it would be annoying if you had to retune it between every song.
With relative pitch music sounds the same even if you deviate from the original equal temperament pitch of the key you started singing even changing the key.
For the same reason if there is a fixed instrument playing at the same time, like a piano accompaniment, it's sound would be used as a reference and the singers would not drift