MB 124.1 - 124.2 The Repetition of the Amidah by the Chazan

The repetition of the Amidah was instituted primarily as a way to exempt members of the community who did not know the words of the amidah themselves. For this to work, each person needs to listen to each and every word without interuption. The ability of the chazan to exempt another person does not work if they have the ability to pray the amidah for themselves.