A long time ago, I decided that I wanted to make web pages and put them on the Internet for some reason. I picked up a book called HTML 4 For Dummies1, made my first website about nothing in particular2, and showed it to the world. The book was a nice gentle introduction to HTML, and the first page was a tearout color chart (printed in actual colors!) that gave you hex codes for a selection of colors that you might want to use (and a lot of codes for colors that nobody would ever use). There was also a whole page devoted to picking colors and divining their hex codes or going to web pages and stealing their color codes if they used a color that you liked.
That's all fine, but I'm not much of an artist, and trying to tweak shades of red, green, and blue is tedious to me. Sure, having the fidelity to be able to choose a particular shade out of the 16,777,216 available colors is, frankly, amazing and a little bit daunting. It turns out that just about every web browser on the planet that supports colors also supports a winnowed list of 141 colors that have names I can remember.3
It's really easy for me to mock up a little bit of HTML (or XML), apply some style to it, and play with the colors without having to resort to using a color-picker or some web-service if I just want orange text or a brown border. I don't know about you, but I find 'orange' and 'brown' easier to remember than #FFA500 and #A52A2A, respectively.
I guess I might care a little bit more about using the full gamut of colors if I was trying to do something more complicated than what I'm doing here. But since I'm not, I don't.
There's also the small matter that virtually nobody uses named colors for their website, which, for me, is as good a reason as any.