I totally agree with this, personally I put weight in story more but as you said:
If it's Bad then why would you want to see the Story of a game that Plays Awfully.
And the best games are the own WHO explain the gameplay weirdness and flaws in a way that fits the game story. (The game I'm playing now, Disgaea did that to some extent.)
Of Course There are always Exceptions, Games without a Story can Work if there is enough Replay Value, Hell my Favorite game is Terraria, and that game's Story is only Mentioned in Optional Text boxes, and that game is fun because of how much Replay Value it has.
Yeah, I can think of some games like that too.