Ninja Gaiden 1 was very close to getting a PS2 release at some point believe it or not, there's even a PS1 magazine that mentioned it on one of it's covers back in 2000. I guess Itagaki knew that blood and bobs were going to look, and perform better on Microsoft's first console.
Just because Tifa's in Dissidia doesn't mean she should be in DOA lol. She'd be like 30 bucks or more on PSN. Maybe 12-15 bucks if she was on T7. Let's also not forget Noctis's appearance, and that PS1 game from the 98-99. There is no way in hell Tifa will appear in DOA6. It's not like you give a shit about Dissidia anyways.