Searching commanders should have an extra chance (maybe modified by the current luck scale) to uncover a magical trinket in addition to the searched sites:
I do like magical trinkets, but it is hardly worth the gems and mage time to forge them! Furthermore, I love it to find magical items after a battle! Anything that I can get is fine - it just appeals to my primordial greed to seize something as my prize for winning a painful, bloody battle!
However, my enemies rarely field any item-wielding commanders besides SCs. So why not making low-level items more abundant by such a mechanism? Adding such a mechanism would also increase the luck scale's usefulness (especially if there would be more cursed magical trinket to be found besides the odd slave collar, hehe!).
However, I would oppose the idea that a search and a high luck scale could produce anything better than a lesser magical item or even extra gold/gems in order to avoid an exploit of the luck scale by heavily searching and re-searching...