|laziness, impatience, and hubris|
I don't think it's a good idea, and I'll try to explain why. The same reasons essentially apply for complete syntax highlighting.
It would be neeed to enforce that inside <CODE> elements one could type Perl code, and Perl code only. Otherwise the highlighting would be just noise. I've just used it to enclose HTML for example, where # is not a comment character.
Coloring in HTML is done through lengthy <FONT COLOR="#RRGGBB">...</FONT>, this would make pages longer with subsequently longer downloading times. It's certainly a minor problem now, thanks to style sheets in HTML 4.0.
It's probably unnecessary for short snippets, whereas for longer one it's always possible (and quick) to download the code and use the editor of choice. It's what we usually do anyway, when we need to take a deeper look at the code and maybe run it.
It would spoil some obfuscated code, or worse, it would not work correctly with it.
Just my two cents. No flames, no criticism :-)
Update: thanks to John M. Dlugosz for pointing out the STYLE attribute approach to colouring text in modern HTML