The story centered around the ninjas' conflict with DOATEC, so if anything, we would probably get more emphasis and details on Ryu's role.
That said, I recall there have been some interactions where the combatants seem familiar amongst each other, so it could've been nice to have moments where they actually communicated in the first tournament. They could show us a build-up to Tina and Lei-fang's match in DOA2. Shoot, it could've been nice to see Tina put on or pull off a brown wig before/after the tournament.
As far as Kasumi, it would've been nice to see her face some setbacks, because Hayate, the next planned head of the Mugen Tenshin was recognized by his father. Kasumi was a back-up plan in the line of succession, meaning Hayate was stronger than Kasumi was at the time and still lost to Raidou AND Ayane. If Kasumi struggled to get to the finals, it would've shown a clear progression of skill that you wouldn't see in contrast to Kasumi blitzing everybody to the fight against Raidou. It would've also provided a reasonable justification for Kasumi to defeat Raidou, instead of her needing a Ryu Ex Machina to salvage the event.
I suppose at the end of the day, we just needed more scenes for DOA1. They could not have made it more obvious that they wanted to get that part out of the way, but another big issue I can think of is that the tournaments never actually held much significance in itself. The tournaments have always kind of just been there, but it never added anything to the story. In fact, the tournaments could've been removed and nothing would've changed.