If people are going to view your graphics over the web while using displays of varying color accuracy, that is all the MORE reason to create the graphics on a system where you are seeing the true color. If you create a graphic on a display that (for example) de-empasized the blue color channel, then you are going to tend to push the blues harder to "make it look good". Then, if a user views the graphic on a web page via a display that over-emphasized the blue channel, guess what? They will see something that's ridiculously blue-shifted, WAY off from what was intended by the creator.
This is the same reason that music is mixed using speakers with as flat of a frequency response as possible. Even though almost none of the stereos that will be used by consumers to play the recording are anywhere close to flat in their response, that just makes it even more important that the original mix be as neutral as possible, to avoid having the mix skew WAY off kilter on some end users' audio systems. Graphics should be treated in the same way, IMO.
There are a couple of LCDs in my household in addition to one fairly good CRT (Mitsubishi DP930SB), and my CRT absolutely smokes the LCDs in the area of color reproduction. Personally, I'd never consider creating graphics for any professional or even semi-pro purpose on any of the LCDs I've seen. I hope there are some high-end LCDs that do a reasonable job here, but I dare say that they aren't going for a price anywhere close to the $269 that my ABSOLUTELY ROCKING CRT came to my doorstep for.