Item Level? I'm not clear

[Nezerius]

But none of that appears to answer the question. If you add stuff to the item, or craft a better item, why doesn't the item level just change to reflect the new stats?

Because it would increase the stat caps past the amount that the devs intended for that item.

The item level determines the stat caps on an item. For example, an iLvl 380 crafted healer robe would have a stat cap of 301 crit. The NQ starting at 190 crit, while the HQ version starts at 211 crit.
Increasing the iLvl would also increase the stat cap. The devs intend for a piece of gear to have a specific stat cap.

It's also possible that:
Their system simply isn't able to have two of the same items with the same name, but different iLvls
-and/or-
Their crafting system can't give out one of two different iLvl version during a craft (for example, i380 NQ/i390 HQ from a craft).