String hit the nail on the head about the soul being easily (I use the term loosely here) resurrectable while it’s still in the Veil. Once it passes to the beyond, it becomes more difficult to resurrect someone, often requiring elaborate rituals like in the case of Calia and Lei Shen. Soul stones seem to operate on this same logic by intercepting the soul.
Moreover they confirm this in Before the Storm as it’s pointed out resurrection is considered possible within moments after death – and Anduin being unable to resurrect Calia in the moment after Sylvanas’s Death™ arrow was considered Very Weird. She was too recently slain for her soul to have passed that fast, later necessitating the weird Light Undead ritual with the Naaru.
As for “who” can resurrect with the Light? In the old Blood elf Paladin class quests, it’s pointed out that every member of the Blood Knight Order must master the art of resurrection before they’re elevated to a fully fledged member of the order. It’s their final trial to show their mastery of the Light, but also their devotion to the order, as the person they’re resurrecting is always another Blood Knight. Failure means the death of a brother.
That being said, Blood Knights (at least fully fledged Knights) aren’t a regular footsoldier unit either, but the elite in their own right. But the same goes for Paladins with a capital P as I’ve laid out in the Clerics & Paladins guide I wrote last year two years ago detailing the differences between Paladins and Clerics in lore with citations:
In short, a Paladin with a capital P is more than just a priest in plate; they undergo a ritual of empowerment with their clergy becoming reborn in the Light as their champion. Someone who has earned that (and indeed, RPs being a Paladin ‘properly’) is someone I could see being able to pull it off.
But most importantly, as many have pointed out: resurrection is a plot device first and foremost, and it needs to fit the narrative. Character death can be an impactful moment, and undoing it can actively ruin the moment. To bring them back to life ought to fit the narrative you’ve set up.