Are designers who can code "more valuable"?
That depends — in particular, on what type of designer you’re talking about.
I’m glad to see Benek re-broach this topic, because a fresh perspective on the subject can remind designers to consider rounding out their tangential skills. Especially skills that could extend their current primary skillset. The dividends, can, quite literally pay for themselves.
The value in being a modern designer who knows code isn’t that you can replace the job of a front-end dev…but that you know the ins and outs of it. It’s about understanding what developers are talking about so you can participate in discussions that cross between design and front-end.
If you’re a designer “hired to do an array of jobs on a project” then you can expect a bump in the value you present individually to the business/team you serve.