I did do a quick test. My process was to film a white wall as a 4k Raw clip, which I processed into a 4:2:2 10 bit uncompressed file. I then used ffmpeg to process the uncompressed video into two different clips with the only difference being the bit depth. I used 420 color and crf 16 on both. The two files both ended up roughly the same size. (8 bit is 3,515 KB, 10 bit is 3,127 KB).
I applied a fairly extreme amount of gain, and white balance adjustment equally to all clips. I've included a 100% crop of the uncompressed, 10 bit, and 8 bit files. As you can see, the 8 bit has significantly more ugly banding than the 10 bit.
As you can see, the 8 bit has some nasty banding that is not present in the 10 bit version. This is of course an extreme example to show a relatively small difference, but also it does get perceptually worse in motion rather than still frames. Also note that the PNG files themselves are 8 bit (which would match a typical delivery). The banding you see is from the color grading, as all 3 versions have been quantized down to 8 bit upon rendering.
Moreover, the 10 bit is actually a 10% smaller file. I find 10 bit HEVC is consistently a smaller file size than 8 bit for better quality. The real benefit of more accurate sampling is that it allows more accurate processing throughout, from compression to coloring.
On an related note, both the HEVC clips have lost all the grain and detail compared to uncompressed, which is very unfortunate. However, they are 1% of the file size so I can't complain too much!
Edit: just look at the file names to see which pic is which