Are there still web designers who don't know how to code HTML and CSS? I haven't come across one in a while and would probably never hire one, so that's reason enough to learn how to code.
But consider the fact that many coders don't have the most basic grasp of design. Not even really fundamental things like alignment, proportions, which colors go well together, or even how to phrase a sentence so it makes sense to the user — which isn't even design, it's just english.
I think it's kind of a jerk move for coders to expect designers to like or care about coding, even really simple fundamental stuff, when many coders are notoriously lacking in the design or even taste departments.
Having said that, it is obviously a huge benefit for both coders and designers to at least know the basics of the other's trade.
One could even argue that you're not really a truly talented developer nor designer until you do; but, before we come down on designers, let's look at the state of design skills in the coding community.
But have you not also worked with coders who are fundamentally inept at design, making it seem like they're almost blind? I know I have, but for some reason we seem to more often accept this kind of very similar lack of tangential skill level.
Functional and elegant rarely equate to a designer as they do to a coder. For example, I know that many of them would really dislike Hacker News. Not enough, "pop" or "zing" to it.
My point is simply that before we complain about designers lack of coding ability, perhaps we should first educate those in our own trade about the fundamentals of design — because coders are no better at this. Glasshouses, and all that.
Lots. Big agencies I know of have designers who spend all day in Adobe products and don't touch the code. These are the people creating official sites for movies, video games, Fortune 1000 brands, etc.
So it depends on where you find web designers: If it's through blogs and such, then yeah, a bigger percentage of them will also do front-end code. But from my experience, agencies tend to compartmentalize.