If Hearthstone has a fundamental issue, it's the usage of the WoW classes as their replacement for a "color"-type of system. Anytime you print a class card, Blizzard has to ask themselves if the card is thematic to the class.
In WoW, you don't necessary care if the classes are "balanced" since PvP is not the primary focus. You just have to consider different playstyles and make each class worth playing. But in Hearthstone, balance is a much bigger issue. This conflict between WoW and Hearthstone means that some classes in Hearthstone have a much wider design space than other classes.
For example, in WoW, Shamans could basically do everything. They had weapons. They had healing. They had damage spells. This gives the Shaman class in Hearthstone a HUGE design space. You can have a Shaman deck do basically anything and everything all at once. Except gain armor, I guess?
Take Rogue as a counterexample. In WoW, Rogues were a class that snuck up behind you, waited for an opportunity, then busted in your head in with a flurry of attacks and killed you dead instantly. They were squishy as fuck, though. This is represented well with the Aggro and Miracle archetypes of Rogue. But what else can they do? Rogues aren't really known for healing, survivability, or taking down swarms of enemies all at once. So they aren't supposed to get strong heals to counter burn or strong AOE to counter large numbers of minions. So Control Rogue just can't exist. Rogue is locked in to fast or "tricky" strategies. That's a much smaller and much harder design space. You keep seeing Blizzard try to use the "thief" aspect of the class recently so that their brains don't have to work so hard, but getting random cards from your opponent's class is not necessarily compelling design for a card game.
To Dahbomb's point, Hunter kind of falls into this trap because Hunters in WoW are all about safe, consistent damage. You toss out your beast friend in front you, then plink away with your bow or gun. If the enemy gets too close, lay a trap. To the extent that WoW hunters could "control", it was mostly about the traps and evading the damage in the first place. Hunters relied on their beasts and their traps to get out of harms way. So I dunno, if you want a Control Hunter, maybe what you have to ask for is better taunt beasts? Or maybe print some better secret cards, like a Hunter version of Hydrologist? Hunters will never have ways to counter burn (they don't heal or have strong armor), which makes any kind of anti-aggro or control deck sketchy, because most control decks need ways to counter both minions and burn, not one or the other. So, Aggro and Midrange with beasts it is.