I play Starcraft for the story only, and I loved it. Still play the campaign from time to time. I feel like a savage amongst civilized men on this thread.
This was how I played AoE and StarCraft as a kid! I think the vast majority of players play them this way, actually. If you're in the competitive multiplayer scene, it's easy to forget there are millions or tens of millions of single player / campaign-only players.
Campaigns seem to have a bad rep among most gamers online, but honestly they are the most satisfying aspect of strategy games. One of my favourite games growing up was Rise of Nations and its Conquer the World maps - remove that and you get a worthless husk.