…they don’t though. Aggro DH, hunters, and rogues beat priests in general. Priest control tools aren’t enough to stop the fast and consistent pressure of the former two, while rogues have resource generation to let them dump without going out of steam.
What priest punish are actually those that DON’T do what you say. Priest punishes decks that try to win by steadily gaining each turn with good trades and resource management. AKA the midrange tempo decks of old.
They’re the ones who don’t have the pressure as fast or consistent as DH and hunters, so a priest has enough breathing room to survive into late game.
They’re the ones who need to build board to do damage unlike DH or hunter… but then doing so means they’re punished harder by priest board wipes, which they can’t recover as well as a rogue with resource generation.
They’re the ones who (after failing to blow up the priest first) don’t have enough control tools or resource generation of their own to deal with priests in the long game, again unlike a rogue.