Yeah, I think that was my favorite take on the arcade style story mode that catered to each fighter.
Prologue > Three Fights > Special Fight 1 with pre and post fight cutscenes (and a select few special cutscenes for losing) > Four Fights > Boss Fight with pre-fight and post fight cutscenes (the same for several characters) > Ending Movie (sometimes with an Epilogue beforehand).
A select few characters had two special fights (like Lei), but overall it offered something for everyone. Tekken 6 and 7's story content for anyone who wasn't the very main cast was pretty dire, though at least Tekken 6 had unique pre-stage text for each character in Scenario Campaign. Tekken 7 just gives you one shitty cutscene per fighter.