COULD it? Yes.
WILL it? Doubtful.
SHOULD it? No. Trading absolutely ruins online card games, even when it's allowed from the release of the game.
Not sure if you're familiar with this game or not, but I'll explain briefly how trading works in Star Wars Force Collection:
1) A large group of the community immediately gets together and discusses every Legendary card, and comes up with a tier structure. Top tier cards cost you the soul of your firstborn in card value. High tiers cost you both arms and legs. Mid tiers cost you an arm and a leg. Low tiers you can actually trade for, but aren't that effective. Trash tier are Legendary by rarity only, and have next to 0 value.
2) People devise a way to sell the cards for real money outside of Hearthstone, which creates a massive market in which players pay each other as opposed to the company that created the game (and yes, a lot of players jump on that bandwagon because buying an individual card that you're guaranteed to get is cheaper than buying packs), which leads to scammers jumping into the market to screw people over either by a) not providing the card once they get the money or b) paying someone for a card and then arguing the purchase on PayPal and getting their money back (while still having the card).
3) When a new Legendary is released, the people that get the card within the first week or so refuse to trade it unless you're willing to sell your soul and the soul of your entire extended family (not to mention the ridiculous number of in game cards they want as well). As a for instance, say Blizzard was to release Arthas Menethil as a new Paladin Legendary. The people that pulled him immediately (and for a good while) after his release more than likely wouldn't take less than Dr. Boom, Tirion Fordring, Lord Jaraxxus AND Mal'Ganis (and that's if you were lucky enough to get it THAT cheap from them).
The current dust system is fine, and is actually better than most other online card games (if not all, though I can't actually make that claim as I haven't played every online card game out there). Even if you never pay a dime, you can eventually craft the entire collection of cards (golden cards included), AND there's no subscription. Hearthstone is completely free to play.
Does it take a while to craft even one legendary as F2P? Sure. Does it take longer than buying packs? Definitely. But you are still able to craft the entire collection whether you pay or not, whereas games like Star Wars Force Collection, you could play for 100 years as F2P and never see a 5 star (the equivalent to a Legendary in Hearthstone), and you could also spend Bill Gates' net worth in real money buying packs and never see one either. I doubt it would take even remotely 100 years to craft the collection (gold versions as well), and if you're P2P, it wouldn't take you anywhere near Bill Gates' net worth in real money to get the dust needed for the entire collection.