Namco tried a version of that with Soul Blade. I don't know about Tekken, but Soul Blade on the PlayStation had a "story" mode which was a really clever way of putting a storyline around a sequence of fights. It also earnt you extra weapons that you could use in the main game.

I wish they'd made more of that; they could have turned the story mode into an animated movie or even a TV series. I would've watched that!

Wade.