Knowing how to build a web page lets you begin to grok how the web works. A better understanding the medium will produce better results, in general.
In practice, however, in a startup working on an app of sufficient complexity, it's not scalable for the creative to be designing and coding at the same time. More time spent fidgeting with HTML means less time iterating on UX and aesthetics. At some point, someone needs to completely own the design.
My personal experience is that a prolific dev team will easily backlog you with features that need UI. I often have to run with my first or second mock-up because time is so critical.
All that said, I can't agree more that designers should learn to code. Print isn't dead yet, but at some point it has to get there. Being fluent in new media is about survival.