I'd like to bring up 
He's a champion that has healing as part of his kit, and it makes him a unique threat on the battlefield, much more differently than other spellvamp/healing monstrosities (
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He's had some very distinguishable problems in the past - Namely that he was slow, immobile, and short-ranged compared to other mages. Building Magic Resistance also entirely negated his usefulness, as his healing was based on the damage he dealt. Ironically, this also caused him to heal absurd amounts against teams that didn't get MR. Riot responded to this by reducing his overall healing, making his damage more reliable (It used to be RNG on his ult), and making his healing not dependent on his damage dealt, meaning MR stacking no longer gimped him.
Grievous Wounds is a -really- awkward thing in the game. I'll often see a top-laner rush Executioner's Calling to counter me, but this simply puts them behind pre-6, allowing me to roll them over entirely. Lategame however? It's fucking cancerous, as Swain often gets bursted down and needs to heal back up, but can't simply because GW has probably applied at this point, especially with the amount of champions who build Morrelonomicon. It applies even while Zhonya'd, reducing the effectiveness of what is pretty much a mandatory build path on Swain.
Swain needs healing to exist, and is very thematic to him. Grievous Wounds exists to make sure champions like him stay in check, but it does so in a way that is -entirely overbearing-. Especially if you are already behind. Since Swain's healing is in a state that is -honestly- pretty balanced and has a fair amount of counterplay (Namely, don't let him run amok in the middle of your team), Grievous Wounds reduces his healing to a subpar point where he cannot fulfill his role as an off-tank.