I think they can write good plots for some of their content, though I think it depends on the writer. I'm pretty sure they've got a large writing staff, and the quality will vary from person to person.
I loved the story of Warcraft 3, and to this day, still think the Horde campaign was badass, especially the final cinematic. It was such a wonderful crowning jewel on the game's story, that I didn't even bother playing the Night Elf campaign, because fuck those treehugging hippies. Nothing can top the emotional impact I had from the Death of Hellscream cinematic.
There were specific quest stories in WoW that I thought were brilliantly written, primarily a quest in the...I think it was the Eastern Plaguelands, though it might have started in Western, where you go through this huge quest line to try and redeem the soul of one single man. He was the champion defender of a village during the initial Scourge invasion, and he successfully fought off and defeated a lieutenant of Arthas and his horde, with the help of the villagers. But he was wounded in the fight, and turned into an undead overnight, and then killed the village he saved. A dragon of the Bronze dragonflight, sends you on a long quest to try and gather items from the fight, that have "spectral/temporal resonance" so that she can use time magic to basically reinact the battle, but this time you help the fight, and try and change the outcome among the ghostly combatants. If you succeed, the spirit of the man is redeemed, and he's able to finally find rest. It was just fucking awesome. I don't know which writer came up with that one, but I love them to death.
I FULLY agree with your opinion of Heart of the Swarm however, and I was just bitching about this fact to a friend of mine last night. It totally negated all the effort you do in Wings of Liberty, and it REALLY pissed me off. "What? Kerrigan isn't the iconic and really popular Queen of Blades anymore?!? Fuck that!! Retcon that shit and get her back into her freaky/sexy look for the fans to drool over!" Bleh.
I think the story in HotS was...ok. I mean, it was decent enough to actually motivate me to play as the Zerg, which I don't really like to do. But it felt forced, and when it was all over, I just was like "Ok...so um...yeah...that was a thing...that happened....yay I guess?...we won?"
But, to be fair, I've never really been heavily invested into Starcraft as a player. I mean I played it, I liked it, but the story of it never really sucked me in like some people. I enjoyed it more for the gameplay, and was happy that the story was fairly decent.
I think they have their moments of quality writing, but when you are talking about a company that has been putting out content for what...20 years now? 30ish? You're not going to have A list quality writing all the time.
Though I do think they do dramatic cinematics like nobody's fucking business. They always suck me in with how epic they are, and the emotional impact of them. Top notch on that front.