The site is literally about CSS color names for 256-bit colors, it’s not a palette site with beautiful colors. This is a ridiculous feature request, but I can’t say I’m not used to this.
This may be a use case perspective. For your use case, knowing hex code is superfluous, and that is your mental model. I interface between researchers, designers and developers. If someone in my environment says "I want this cadet blue', the first thing others ask is "what is the hex code".