I think splitting it into three games did effect the single player, there was only really enough plot for about 8 missions, the rest was mostly filler. And yeah, video game writing as a whole is not good, but I felt much of the writing in the game was poor even by those standards.
I do wonder how Heart of the Swarm is going to handle things considering how the game ended. I'm not sure if it will it be concurrent with the Terran campaign or a "sequel."