I think people want to be good at what they do. The best designers can either "waste time" on becoming novice programmers, or they can perfect their core craft. If they spread too thin, they might soon stop becoming the best.
I guess it also depends on the role you play in a company or start-up. If you can help out other teams and communicate, that is very useful for a start-up or small business, but not something I think is appreciated in some larger companies: You get judged and hired on one core role and are expected to do that very well. If a big company needs design, they likely hire a full-time designer, not ask that DBA with a keen eye.
I am sure there are a few hack-of-all-trades that mastered full webstack programming, data analysis, community management, marketing, SEO, usability, copy-writing, design etc.. But I also feel it is unrealistic to expect one to be able to switch to the other, regardless of their individual talents and expertise.