Avoiding arbitrariness is useful to epistemic rationality and therefore to instrumental rationality.
Avoiding giving credence to arbitrary beliefs is useful to epistemic rationality and therefor to instrumental rationality, and therefor to goal G1. Avoiding arbitrariness in goals still does not help with achieving G1 if G1 is considered arbitrary. Be careful not to conflate different types of arbitrariness.
If an AI has rationality as a goal
Rationality is not an end goal, it is that which you do in pursuit of a goal that is more important to you than being rational.
Avoiding giving credence to arbitrary beliefs is useful to epistemic rationality and therefor to instrumental rationality, and therefor to goal G1. Avoiding arbitrariness in goals still does not help with achieving G1 if G1 is considered arbitrary. Be careful not to conflate different types of arbitrariness.
Rationality is not an end goal, it is that which you do in pursuit of a goal that is more important to you than being rational.