To be fair, this sort of applies to retina displays as well: The hardware put into some of the Retina macs can barely handle the bandwidth demands of realtime rendering at such high resolutions. Until that problem is addressed, you certainly shouldn't be running around demanding >8bpc color precision.
Dithering for gradients could certainly make a minor difference in rendered quality, but I don't think most browser vendors are interested in making rendering performance slower right now - they're quite busy trying to make it faster. As evidenced by the fact that the OP's site runs like complete garbage in even modern browsers. Even if you spend the cycles and the power to dither, you're basically approximating something like another bit of precision. Is it really worth the cost just for another bit? You could support the argument for dithering by showing a side by side comparison, at least.