Shaders and Textures should not be dissociated because then that type of discussions ensue 
They are the two faces of the same medal.
I will try to put it another way: An albedo/diffuse texture is nothing less than a coloured plane normal to the optical axis of the camera and illuminated with a light aligned to the optical axis, i.e. an albedo texture is merely a special case of shading/rendering. It might as well be an emissive plane rendered in the scene. You would surely not review a rendered image without a View Transform? No! I know that you would not, at least not today after having roamed weeks on ACEScentral 
And remember:
ACES images are not directly viewable for final image evaluation, much as film negative or files containing images encoded as printing density are not directly viewable as final images.
If the Display Referred Non-Look Look of your textures is the Look you want to see when authoring them, you are, again, absolutely free to do so. You will most likely not be able to do that in any major studios nowadays though. And, as I mentioned it, you will not be able to get that Non-look Look under the View Transform when producing renders anyway, never ever
I will not venture into the colour picker territory because it is too complex and contextual (depends what you pick, how the colour picker is colour managed, etc…) and will only serve to complexify an already complicated discussion.
I would be keen if you were able to share some images of what you are looking at, cartoon is a broad category and maybe it would help the discussion.