The reason you have two engaged on approach is because it is a duplex system. Two radios listening to the ILS with two a/pilots with two power supplies monitoring each other.
If the two channels differ then the system drops out with a warning as it is not safe to continue.
Once you have gone around then there is no need for two channels any more as there is no longer a radio signal to be monitored, one channel is sufficient to maintain heading once selected, and control the pitch and speed bugs.