With Standard bringing a new way of playing and some fresh air to the game, also come the fear of the fear of losing some cards, and i believe could each year add a couple class cards from the rotating sets in the standard roster, while this being a dangerous move i believe they should only add cards that somehow became a part of the class identity and not cards that are usually powerfull in that class, one example for this is Quartermaster that is a card that is not considered as powerfull it can still support paladin hero power and then being a powerfull card to support the identity of the class, on the other hand a card like Lightbomb for priest even being too powerfull is a must of on the class and then needed to be added to the current roster to make the class on par with the others.
Here are the cards i believe could be added that would not in any way make the class stronger and still would make the identity more clear
Voidcaller might be a very powerfull card but that is the main enabler for demons and with blizzard saying they are going to print more of then this card would fit the theme and enable more powerfull demons decks and maybe someday people stop the zoo madness, now darkbomb is not as powerfull and probably a very important card for control warlock decks and that would be a very nice on standard roster
the other alternative being Death's Bite and warrior with another powerfull weapon it would become the most powerfull deck around and we dont need that and shieldmaiden a powerfull card but not overpowered in any sense
I generally agree with the idea that a few non-Standard cards should become part of the permanent set. Where I disagree with the OP is that I don't think every class needs a card, at least not for the first move. Instead, some classes need immediate help while others need nothing. If they need to keep the class-specific card pool identical, maybe every class gets 1-2 cards initially, but some classes get garbage.
I also think a very limited number of neutrals should come into the classic set, but only ones that provide a mechanic that is unique and desirable, the replication of which would just feel like a reprint.
So, with all of those generalities said, here are my specific ideas.
Druid- Does not need significant help. Current Wild Cards into Classic Set - Yeesh. Um, Poison Seeds and Druid of the Fang (as OP suggested) BRM/TGT/LOE into Classic Set - Darnassus Aspirant (ramp is clearly a permanent Druid strategy based on the core kit) and Living Roots (closest thing Druid has to a class 1 drop).
Hunter - Does not need significant help. Current Wild Cards into Classic Set - Webspinner (Beast archetype is core, and helps address class weakness in lack of draw power) and Feign Death (permanent support for Deathrattle archetypes) BRM/TGT/LOE into Classic Set - Quick Shot (2 mana, 3 damage with some benefit is a fairly typical card across classes, provide some early game removal in case control hunter is ever a thing) and Bear Trap (decent all around secret + beast).
Mage - Does not need significant help. Current Wild Cards into Classic Set - Echo of Medivh (Mage doesn't need a ton more support and this pushes a control/fatigue archetype that is more or less dead now) and Duplicate (screw it, let's go full fatigue mage) BRM/TGT/LOE into Classic Set - Forgotten Torch (burn spells are a core card type and this one is unique) and Rhonin (never really saw significant play but could find its place in a slow enough meta).
Paladin - Could use a little help Current Wild Cards into Classic Set - Quartermaster (good idea, OP) and Coghammer (okay weapon with minion buff helps now-weak early game) BRM/TGT/LOE into Classic Set - Keeper of Uldaman (I really hate this card but it fits the class so well) and Solemn Vigil (anything to discourage Divine Favor, really).
Priest - Needs massive help Current Wild Cards into Classic Set - Velen's Chosen (helps address limited early game, fits well with buff and heal strategy of Priest as well as AOE) and Lightbomb (another good call by the OP) BRM/TGT/LOE into Classic Set - Entomb (yes, people hate it, but it's powerful and fits with the feel of the class) and Flash Heal (good synergy with Velen, flexible card). Strong honorable mention for Vol'jin here.
Rogue - Needs some help Current Wild Cards into Classic Set - um, yeesh, again Tinker's Sharpsword Oil and Goblin Auto-Barber (lack of other choices) BRM/TGT/LOE into Classic Set - Dark Iron Skulker (AOE, with Rogue lacks) and Anub'arak (great fatigue card if Rogue could ever get enough control support for it to be a viable archetype).
Warlock - Doesn't need much Current Wild Cards into Classic Set - Voidcaller and Darkbomb (see OP), Mal'Ganis (just such an awesome legendary, all other non-Jaraxxus Warlock legendaries suck, Demon synergy) BRM/TGT/LOE into Classic Set - Imp Gang Boss (great card for multiple archetypes)
Warrior - needs nothing Current Wild Cards into Classic Set - Shieldmaiden and Iron Juggernaut (Shieldmaiden is powerful and generally useful, Juggernaut really only works in fatigue match-ups) BRM/TGT/LOE into Classic Set - Cursed Blade (Warrior has too many nice things, so this is its cross to bear, plus it's a slight nerf on all random weapon generators for the class) and Bolster (because one day taunt Warrior will be a thing, I swear...)
Neutrals - Emperor Thaurissan - unique combo enabler - Antique Healbot - powerful neutral heal - Loatheb - much beloved neutral spell stopper - Deathlord - beefy early game taunt with a real downside, could help slow the standard meta - Sir Finley Mrrgglton - facilitates deck construction outside of each class' core archetypes - Stoneskin Gargoyle - Blizz is always good for one completely inexplicable decision Honorable mention - all of the dragons and related cards. On one hand, rotating almost an entire tribe out the game feels a little sad. On the other hand, maybe we don't want dragon decks to be a permanent meta presence
I really like the ideas, the other thing i was thinking is the possibility of reprinting a Neutral class that is genarally only used on a class and make it a class card, for example reprint Zombie Chow and make it a priest only card, or something like that because we all have at some point saw one card that is powerfull in one class and dont do as much on other, i believe that might be something great, now about Loatheb/card] and [card]Brann Bronzebeard, i think legendarys like that should be a core part of the game because they support a core mechanic of the game and that should be a part of standard as a whole
I don't agree with all the additions. I feel we should only add the bare minimum to keep a class working because it have flaws or because it's the only thing that allows an archetype to work. Stuff like Shieldmaiden shouldn't be included. It's just a good drop with armor. There is that for C'thun Warrior, and it doesn't really do anything exceptional. Bleh, not good enough to be added to evergreen.
I agree with stuff like Voidcaller for example. It's amazing and really should have always been there. It allows Risky deck building for Warlock and has some great plays that you can pull off. But there is also the problem that it can bring back the work demon on your hand. It's absolutely great.
I totatally agree with keeping Deathlord, and I'd go even as far as adding Zombie Chow to the neutral list. These two cards allowed Priest to work. They removed the ability for everyone to play sticky/difficult to kill stuff if they were control-ish or waiting to curve out. That's why Aggro is so strong. Zombie Chow could trade for a couple of Shaman's minions without being interesting for aggro to use. Heck, Haunted Creeper could be used by aggro and non-aggro but it slowed down the game so people wouldn't die on turn 6 for Doomhammer or Leeroy combos.