I'm also all for inspiring leaders. But in the startup context, I think the job of "designer" is as dangerous as its technical equivalent "architect". As Schell points out, design is a pervasive concern, just like software architecture is. A CTO who fancies himself chief architect is likely to drive off good talent, because talented people want to solve whole problems, not mechanically execute somebody else's vision.
I think the same applies for the visible sorts of design just as much as it does for the under-the-hood design: if everybody cares (which requires feeling empowered to make things happen) you'll get a better product.
Care to justify that statement with evidence?
Or do you think that only back-end code will make your hands dirty, and not research, requirements gathering, ensuring the product does what paying customers want and expect, customer support, analyzing, categorizing, prioritizing customer feedback, analyzing usage statistics to divine customer intent, creating and managing a/b tests, writing road maps, defining feature sets, managing development, html, css, wireframing, testing?
In companies I've worked with, the developers have been sheltered from most of the "real work" of turning their code into an actual business, but simultaneously believe that they are the only ones contributing value. It's cute.
What you're talking about goes well beyond the formal role of "designer". Consider, for example, what happens if you sign up with one of the many outsourced design firms. They won't do most of that. The good ones might do some user research. But that's not guaranteed; what they all promise to do is produce a very pretty document with a bunch photoshop mockups. Which an implementation team is expected to execute as written.
I definitely think developers should be active participants in all that work you describe. (I sure am.) Which is exactly why I encourage people not to have a formal "designer" role. If there's somebody who's officially responsible for X, then everybody else isn't. Design is a pervasive concern.
I think that's a mistake in a startup for the same reason that it's wrong to have a role involving control of quality or security or innovation or customer satisfaction. Those things are pervasive concerns, and if you have one person or group responsible for them, then it means everybody else isn't.
I intensely value design activities and design thinking. And I value products that are well designed. But I think treating "designer" as a role is dangerous.