Gaining quality during a synthesis increases your experience. Most of the HQ gear you get for crafting lets you get much more CP, control and craftsmanship than you get from vendor gear at a much earlier level. Therefore, if you use HQ gear while leveling a crafting profession, you are saving yourself a ton of time and buying/farming materials, because you get more experience per combine (assuming you make your own stuff for leves, etc).

It works the same way with DoW, though more indirectly. If you use HQ gear--if you make your own you save money--you get better stats and kill stuff much, much more quickly than with vendor purchased gear. Thus, you level faster.