Bulking
Gets fiber in your diet
Fills muscles with glycogen and provides energy.
Carbs are of prime importance to gain muscle
Cutting
Fiber allows you to take a nice clean shit
Allows you to have energy filled workouts (glycogen in muscles)
Fiber is also important in fat loss, as is water.
Of course, you could get fiber and carbs from other sources, such as whole rice, whole bread, All Bran etc.
I use All bran cereal with 1 banana for breakfast (and 3 eggs) when cutting. Keeps me awake for the day, fills my muscles with glycogen and keeps me in great mood during my fat loss endeavours.
Dont depend on oats. Theyre nasty (IMO) unless theyre with a protein shake, or milk and sugar or PB. You could go with other sources, no harm in that.