I feel, any good designer needs to understand HTML/CSS, Spot Color, RGB, CMYK, resolutions, and separations. This covers the basics of web and print reproduction.
It's important to understand the restrictions when designing. Without an understanding of how separations work, print design can suffer. The same is true for web design - without an understanding of how HTML and CSS work, web design can suffer.
I don't think a designer needs to necessarily understand any PHP/MySQL, although it can help.
A basic understanding of what Javascript/JQuery does is needed, although actual functionality would be something I'd not really cover were I teaching. Just the concept of dynamic pages via javascript should be understood.
As I'm sure you're aware, web building is really 2 stages - design and development. The more those stages can blur for either the designer or the developer, the better the end result can be. A designer who understands there are restrictions in how HTML and CSS work will not be creating designs that are near impossible to be coded. In the end, I look at HTML/CSS as necessary core knowledge anymore. Face it, HTML has been basically the same for more than 15 years with only minor updates. And it can be learned in a week or less of simply experimenting. There's no reason a designer should not know it.
As for the ads that want everything... They ask for the world realizing no one actually possesses all those skills. But if you leave something off, you may not get that one application from that one candidate with one spectacular skill in that one area. It's a grab bag. No one should feel inferior or insufficient because they only possess a third or three fourths of the listed skills in a classified ad. Most placing those ads are aware that no one can do it all.