My problem with most "serious" game stories is that they try to do way too much. Much more than what the writers and developers of those particular games are capable of delivering. Case in point: Bioshock Infinite. And if we're talking about Mr. Cage, he's the living personification of my point. And I actually enjoyed Heavy Rain. It was stupid, but enjoyable, can't say the same for Beyond based on what I've seen.
For a counter example, I have to bring up Last of Us's story for the fact that it actually had restraint and didn't go overboard when it had plenty of opportunities to do so.