Should designers also code?

My answer: No.
Different question: Should designers also write?
My answer: Most definitely.

Design and writing are more intimately interconnected than design and code. (Do architects also build the house?) If you want to be able to say something with what you’re designing, you have to know what you’re saying before you even think about visuals, typography, color, or layout. A lot of times the process fuses all these things together precisely. If you can’t write, how is that fusion ever going to be precise enough? 

Regardless, in the end, a designer must be able to think* goddamnit. Whether with design and code, design and writing, or design and more design. So whatever that thing is that you boldly strive for in the darkness and in the light, do that, and do it well.

* I’m not specifically talking about the ever-so-popular “Design Thinking Industrial Complex.” Not even close.