Are web-safe colors still relevant?

Since the vast majority of monitors are 16-bit color or more, including mobile devices, does it make sense to even consider web-safe colors when choosing color schemes? Or is it something that ought to be relegated to history as a piece of trivia?

For those of you that don't know what web-safe colors are:

Another set of 216 color values is commonly considered to be the "web-safe" color palette, developed at a time when many computer displays were only capable of displaying 256 colors. A set of colors was needed that could be shown without dithering on 256-color displays; the number 216 was chosen partly because computer operating systems customarily reserved sixteen to twenty colors for their own use; it was also selected because it allows exactly six shades each of red, green, and blue (6 × 6 × 6 = 216).

The list of colors is often presented as if it has special properties that render them immune to dithering. In fact, on 256-color displays applications can set a palette of any selection of colors that they choose, dithering the rest. These colors were chosen specifically because they matched the palettes selected by the then leading browser applications. ^[Wikipedia]

Solution

For me web safe color palette is no longer primary concern. Optimize for the largest target audience.

According to w3schools site visitors:

In January 2009 1% of site visitors had 256 color displays, 95% of users had 24 or 32 bit.
[Update] In January 2015 0.5% had 256 colours, 0.5% had 24 bit and 99% had 32 bit

I found similar numbers from a business app site that I look after:

32-bit  79.01%  

24-bit  15.64%  

16-bit  5.27%   

8-bit   0.08%