I feel with Kokoro they switched it from the kimono for a reason. It was probably due to excessive clipping issues, but I'd like to give them the benefit of the doubt and think that maybe in the end the team decided it was just a bit too bland and generic. I dunno. I'm just not a fan of that one.
On the opposite I like the model of her Doa4's C1 but not too much the dark pink version, while her blue one in DoA4 was my most used oufit for her character (I would like its return in DoA5LR, but maybe it's better to give room to other unique outfits than to a recolour)
I'm not gonna lie, I'd love to see Nyo in the Necrotengu outfit (more than I'll properly articulate with words, and not only because I designed it), but I also recognize that it wouldn't be the ideal C1 for the character as they made her (though it would still be my favorite as I like that evil vibe for boss characters).
The "evil vibe" is exactly the reason because I don't care too much that Raidous' C1 is overall dark and on the opposite I like the idea: people immediately recognize for his appearence that this is a villain, much more than what happens now for the other bad guy of the roster (maybe with the exception of Alpha-152).
And i would love to see your Necrotengu outfit in the game me too, much more than the ideas with whom I come: I hope that sooner or later your wish will be fulfilled =)
That is sort of interesting about Ayane's C1s, though technically I think that she kept the same from DOA1->DOA2 original, and if you count the remakes, she kept the same one from DOA2U going into DOA4.
I don't mind the Legendary Black Falcon being Hayabusa's C1 because I recognize the significance with Ninja Gaiden. But, I definitely feel that his DOA Throwback/Legacy outfit should be available as an alternate in all games, including the Ninja Gaiden games. I'm not sure why they've become so stingy with that one in NG but it worked great in NG: Black and was my favorite outfit in that game, as well as in the DOAs. I was seriously disappointed when I discovered it wasn't in DOA5, and again when it wasn't in Razor's Edge or 5U (before the Legacy DLC).
You're right about Ayane, I was considering her DoA1 but I had completely forgot that her main outfit in Doa4 actually was realized for DoA2U.
For Hayabusa I believe that the matter is that his throwback outfit belong to an age where DoA was heaviliy tied to an anime and Japanese vibe, and in part that outfit recalls to the mind this aspect. With the time the DoA series got always more a different approach adressed more toward serious themes and a sci-fi settings, while NG setted since the beginning a dark atmosphere that permeate all the series (the humor of the NG trilogy is completely different from the one in DoA and much more subtle, is enough to consider how different is the comical aspect of Muramasa with Hitomi). This brough to the consequent disappearence of the Hayabusa's outfit, replaced from the iconic ones of the NG saga (from the blue one of the old NES trilogy, to the white one Joe' style apparently resembling the outfits dressed from the leader of the Hayabusa clan). In lesser measure the process is the same of what happened with the disappearence of Ayane's DoA2 C1 in DoA4.
However, while Ayane's old purple outfit can really appear out of place for the current DoA standards (but I still love it), like you say Hayabusa's throwback is always seemed even to me work pretty well, even for the idea of NG Black to add a mask over it... so I really can't say why they stopped to include it. And however that outfit is so part of the fans' imaginary for the character exactly as for Ayane her Doa2 purple one: undoubtely you will find that the majority of their fans like to play using them, this despite every stilish decision behind the trend to follow with the characters.
Fortunately I think that the addition of Hayabusa's throwback in DoA5U and NGS2+ can be considered an evidence that now we will see this outfit even in the future episodes of the two series.