Are the games worth it just for a story?

I'm not fan of fighting games. While I enjoy them, I get bored of them really quickly because there's not much to keep me going.

It's not just fighting games, I'm like that with video games in general. If there's no good story to keep me going, I stop playing.

Now, if story is good, it doesn't matter how long it Is, I will keep coming back to replay it after some time, just like I rewatch movies that I love.

So, for a moron like me, is story good enough?