I don't think visual web designers should necessarily be able to fully and efficiently implement their designs, but they should have a general understanding of how their designs will be implemented. IMO part of a web designer's educational experience should include interactive design (not just art and print design), HTML and even a programming class.
Likewise, front end engineers should have some exposure to art, design, maybe even have taken some drawing classes, and definitely be able to operate Photoshop and Illustrator (or whatever the predominant tool is).
You don't hire an architect who doesn't already know something about contracting, materials, and geology, even if they're not going to be driving the bulldozer. Same goes for web design.