Combo/OTKs: This should hopefully be pretty self-explanatory. It wasn’t fun when pre-nerf Leeroy was terrorizing the meta, and it sure isn’t fun now. Decks should not be able to consistently do 30 damage in one turn from an empty board, ever. Nor should a deck be able to kill their opponent without actually playing for board. If one of the main decks in the meta can do this, the meta is significantly worse for it. And there are many in the current meta: Grunt Hunter, Cycle Rogue, Handbuff Paladin, Lynessa Paladin, Zarimi Priest, Asteroid Shaman, Wheel Warlock, and Odyn Warrior.
Charge: This mechanic has proven near-impossible to balance throughout Hearthstone’s entire history, whether used by aggro or combo. When designing a Charge card, the developers should ask three questions: “Is Charge absolutely necessary for this card design to function?”, “Does this card interact with your opponent in any meaningful way?”, “Are we sure this card won’t become a key part of an oppressive aggro or combo deck?”. And if the answer to any of those questions is “No”, then don’t print it.
Charge needs to be handled very carefully, as by design, it ignores one of the most fundamental parts of Hearthstone’s gameplay: Minion combat.
Direct face damage/Spell Damage: See Charge above.
Stat Bombs: Cheating lots of huge minions onto the board early is a bad mechanic. The counterplay is awful; either you have the perfect card to immediately answer your opponent’s board, or you lose. There’s nothing in between. Dungar is the quintessential example: How exactly is your opponent supposed to deal with 28+ mana worth of minions when they might not even have the mana for a full board clear, never mind dealing with any Deathrattles? And Dungar is no outlier; Loken, Forge of Wills, Overflow Surger, Razzle-Dazzler…
Overloaded Value Engines: There’s something to be said for cool cards that give a lot of value, maybe even affect the whole rest of the game, but at some point we crossed a line. Even aggro decks rarely run out of resources until well into the late game, and every card feels like a win condition unto itself. Costumed Singer, Gold Panner, Ethereal Oracle, Corpsicle, Sargeras, Kil’jaeden, Helya, Odyn, Shudderblock, Deepminer Brann, Saruun, Gorgonzormu, Unkilliax, Boomboss, Hydration Station, Odyn… the list goes on and on.
And finally, we get to one of the main reasons all of this stuff became “necessary” in the first place, because it has to keep pace with…
Removal: The main reason you can’t just play for board anymore is because it has become laughably easy and often incredibly cheap to clear minions. The craziest boards imaginable, with Deathrattles that would take ages to get through on a good day, can now be Thanos snapped like it’s nothing. A huge minion completely saturated with bonus effects that should, by rights, make it practically invincible will routinely find itself mind-controlled or literally deleted from the game.
And such board-clearing cards often come with major upsides or are incredibly cheap too: Sargeras, Yogg Unleashed, Aman’thul, Amitus, Bob the Bartender, Reno Lone Ranger, Unkilliax, Horn of the Windlord, Incindius, Bellowing Flames, Domino Effect, Fistful of Corpses, Threads of Despair, Table Flip, Reska, the Primus… you will routinely find the board state completely flipped from one turn to the next.