I think Heavy Rain is an important game, yet I understand how some may never get into the game, either for the particular story it tells, or because control, especially at the onset of the game, can break your connection to it quite severely.
There were times that the control had me yelling at my TV in frustration, completely yanked out of the deeper experience I had moments before, but the game is important because it shows how simple gameplay mechanics juxtaposed with context-sensitivity can involve you in a character. It shows how high production forks in story can help make moral choices extremely meaningful. And it raises interesting questions about the nature of its story, and how well the illusion of consequence can be pulled off when the range of emotion is much wider, as it is in games like Mass Effect.
If nothing else, limited control and heavy context makes Heavy Rain an intriguing experiment in game narrative. Perhaps liking it says something about me as a gamer. It delivered better than any BioWare game on the promise of emotional connection in storytelling. I thought about Warren Spector while playing it, who still dreams about creating one last, important game that makes you feel genuine emotion but lets you play the way you want. The range of play in Heavy Rain is less flexible than he might ever approve, but there is a branching storyline with a ratio of production value greater, I bet, than many will achieve with a broader range of emotion or mechanics. If the purpose of Warren's goal as stated is meaningful emotion from a game experience, I wonder how he would feel about Heavy Rain.