If a story is well written, like say Okami or Ocarina of Time, then yes.
The problem is that most of the stories in video games range from mediocre to awful. Normally I like little to no story because most of them are badly written. If it's between a bad story or no story, I'll take nothing.
Also, some games don't need a story. Remember when they tried to write one for Monkey Ball?
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