There are two other reasons, beyond those listed here.

First, Collectables. If you accidently get a Collectable that is not high enough Collectability rating, you can Lower Quality it (down to NQ) to strip the Collectable from it, making it a regular item.

Second, crafting experience. You get base exp for making any synth. You get 50% from rested, 3% from food, and whatever you get from a manual if you are using one. HOWEVER - you can add up to another 300% based on how much Quality you add - but only DURING the synth. Quality added through High Quality items is quality you cannot add during the synth, resulting in a lower maximum experience bonus for using HQ materials instead of NQ.