Yes, I think if the designer is going beyond wireframes, they should probably be doing CSS themselves. Ideally applying CSS to a live prototype that the 'programmer' developed based on the wireframe.
I don't know, I'm not sure what the solution is. But I'm pretty sure it's not PSD-driven development.
I assume when referring to PSD-driven development you mean to say the process of having a designer design a non-responsive, static mockup which is delivered the the front end dev team? I think this is important to clarify because a lot of people tout Sketch as being the answer despite it having the exact same pitfalls and issues Photoshop does.
Check out this demonstration. I really think this is going to be the next big step forwards for designers. I don't think they need to fully understand CSS, the box model, flexbox, the dom, inheritance, etc to deliver effective designs. They just need to be forced to follow these limitations of these things within the design tool itself.
I think the idea is to make every change the designer makes reflect a nearly identical change that the frontend devs are going to have to also make. For example, text color inheritance is a notoriously hard thing for a designer to grasp. If that was handled automatically for them, they are going to out of necessity, create a more code friendly color inheritance hierachy in their designs.
Maybe a "web" designer really needs to know their medium.
A sculptor needs to know about clay and ovens, a clothes designer needs to know how to sew, the strengths and weaknesses of different fabrics and so on (even if Gaultier or Lagerfeld didn't do any sewing and stitching when they made it big, you bet they learned to when they were apprentice designers). Knowing your medium makes you aware of the limitations and possibilities and a better designer.
Why do we insist on coddling designers with tools like Photoshop? What's wrong with making them learn CSS and HTML?
I don't know, I'm not sure what the solution is. But I'm pretty sure it's not PSD-driven development.