I did a creative mornings talk and the biggest thing I tried to say about this subject is "you learn the tools to make the things you want to make". I wanted to make side project websites and not have to pay someone to make / maintain them (knowing they would make no money and I just wanted to do them for fun) so I learned as much as I needed to know to work with existing CMS's and make those projects real.

I think if you are a web designer, it's imperative that you at least know a bit about how to do front end development just so that you can communicate clearly with your developers. I think outright deciding you won't learn ANYTHING about HTML / CSS / JS / PHP, what-have-you, is like moving to France and saying "nope, I'm never ever going to learn even one word of French. I'll just figure out how to communicate by pointing at things".