The number of channels and size of the input image doesn’t necessarily reflect the data domain.
E.g. you could create input images in the shape [3, 224, 224], which would be completely black for class0 and white for class1. Even though these images have a high dimensionality, the use case is really simple and you could create a perfect “model” by just using:
if input_pixel_value > 0:
    return 1
else:
    return 0

As you can see, the necessary model architecture depends on the use case and I would be careful in claiming general statements.