I did some tests on Nuke (compositing software), and couldn't see much improvement downscaling a 4K 4:4:4 8-bit image to a 2K 4:4:4 32-bit (Nuke operates exclusive at the floating point colour depth).
I created a large, gentle ramp and saved as an 8-bit image. The image was reloaded and downscaled to 50%. The differences are a few more pixels were the banding transition occurs. Adding some noise (error diffusion) doesn't alleviate the problem too. We have an image with more information, but it doesn't translate in smoother tonality or better colours.