Why is the NAV ADR 1 ECAM caution a NO GO as per the MEL on the A320?
It is to prepare the aircraft for a possible Emergency electrical configuration. I hope you are aware of the fact that in an A320, if the AC BUS 1 and AC BUS 2 were to fail in flight for some reason, the RAT (Ram air turbine) extends which in turn powers an emergency electrical generator. When the aircraft is in emergency electrical configuration, only the very essential systems are powered and the others are shed. Some of the systems that are shed include the ADR 2 and ADR 3, leaving only the ADR 1 functional. The ADR 1 will continue to supply air data to captain's PFD. In this situation, the first officer's displays goes blank and the captain assumes the flying duties, if the first officer was the flying pilot when the failure occurred.

If the aircraft is dispatched with ADR 1 deferred, and if it undergoes an emergency electrical configuration, as soon as the ADR 2 and ADR 3 are shed, all the flight displays will go off, including the captain's side instruments which are supplied by the ADR 1. Then you will have to rely on standby instruments to fly which would not be the most ideal condition to be in an already crippled aircraft. Remember, this configuration will force the aircraft into alternate law. Both auto pilots, autothrust and even the flight directors would not be available.