2 more:

(1) FC crafting (for airship parts or other stuff) require you to trade in like 10 silver ingots.
Let's say you quick synth'd them, got 9 NQ and 1 HQ. And you don't have more ores to craft another NQ ingot.
If we didn't have Lower Quality option, you'd be stuck, having to buy from MB or go gather the ore.


(2) Your level 50ish Botanist got some Old World Figs as collectibles. However, the collectability is so low that the appraiser won't accept those. So you have half a dozen wasted inventory slots with old world figs that are completely useless.
Collectibles can't be sold for gil or used in crafts, but if you use Lower Quality, you'll be able to stack them and sell them to a vendor, put them for sale in the market board,or craft Fig Bavairoisse with culinarian.