Healing can be affected by Spell Damage if you use cards like these:
You could make the argument that a few healing spells could get the “improved by Spell Damage” card text but making it that all healing is affected by Spell Damage would be a bad idea. That would create some very nasty Priest decks.
Healing is a pointless mechanic in todays HS game. Why? There’s numerous decks that can take you from 30 to 0 in a turn now. So healing isn’t going to be a big deterent.
It’s very good when it’s not wasteful of mana. It’s usually in the form of lifesteal, eg the current meme pala survives a lot of the time because Holy Glowsticks has lifesteal.
It’s also part of why the russian doll demon hunter works, the boars have lifesteal.