It's more about timing and intentions.
Back when they came out with Rondo of Blood, they had just moved to CD, so they decided to include full-motion video. They went with anime, which I think really worked.
For Symphony of the Night, they tossed the FMV, added some dialogue and bad voice acting, and then tossed the FMV back in again somewhat in the form of a good-for-the-time 3D render of the castle. And they went with the very-distinct character art of Ayami Kojima.
Then Iga came into the picture. The GBA games didn't have FMV, mostly because the GBA wasn't well suited to FMV, but partly because Konami and Iga never considered these games to be much of a priority, and FMV is an added expense. Iga was beating Kojima's art style into the ground by insisting that a Castlevania isn't a Castlevania without Ayami Kojima (which is something that simply wasn't true before Iga came along), but since all the GBA could really handle was character art, nobody really complained.
When Iga unveiled the character art of Soma for Castlevania DS, one couldn't help but notice how different it was from Ayami Kojima's art of the exact same character. Iga was breaking his "it isn't a Castlevania without Ayami Kojima" rule. And when asked why, it wasn't so that they could take advantage of the advancements of the DS over the GBA. It was because Castlevania DS was lower on Iga's priority scale than even the GBA games were. Ayami Kojima was "too busy" for this game. And Iga refused to turn this problem into an opportunity, by trying a fresh artist, or including anime FMV in the game. Because both of those things could be construed as threats to his authority, and his rule over the Castlevania series.
Also, there was the instantly-assumed and Iga-approved (since it was convenient for him) "kiddy" theory.
BTW, for those who haven't heard, Iga has apparently heard the complaints, backpedalled a bit, and now apparently there will be some anime FMV in Castlevania DS (which I think has the potential to be better than if Ayami Kojima had provided the character art, assuming they don't cheap out on the anime).
Also, if you want something that's less of an angry conspiricy theory, back in the early 90's anime was fresh, stylish, and new. Nowadays anyone can immitate the typical anime style. So anime has moved on, and is embracing a variety of different styles that vary widely, as most of them are based on manga drawn by different artists with distinct styles. "Generic" anime just doesn't cut it anymore. They need to get an artist with a solid vision behind the animation team. Someone with permission to create and design as he/she sees fit, and would be willing to sign his/her name to that vision. Even if that vision is to be "old school".
But of course, that fits into my "threat to his authority" conspiricy theory, so I don't think that's gonna happen.