You only get 10-bit color with some professional graphic cards, so you will have a computer that only delivers 8-bit color information.
That said, another advantage of 10bit is better picture adjustments on 8bit. Better LUT's.
So it will still benefit a computer that only delivers 8-bit information.
I've seen the difference -- less banding in gradient patterns after adjusting digital brightness/contrast/gamma (in Control Panel).
That said, unfortunately, it likely won't fully help the OP's situation because the banding the OP is getting, especially if the color decimation occuring at a different stage. The OP can test different cards (ATI vs nVidia), different player software, etc. Some brands of BluRay player software do a better job than others. (less banding) It can be worth paying extra dollar for good player software. It could help some, though, as there are many stages where color gradations are decimated. But don't be dissapointed if it has no effect.