1. Value -- a good designer will take the time to understand the the target audiences. Many target audiences aren't looking for value, they're looking for status or something just as intangible. Implementing a visual design which communicates something the target audience isn't searching for is closely akin to pricing your product incorrectly. In fact, design approach is almost completely analogous to retail product price stratification.
2. Trust -- this again depends on audience. Sometimes "labor of love" is the most relevant trust mark, but in other cases it's "well-established" or "industry leader."
3. Accessibility -- this is kind of a 'duh' for any experienced web developer. Most design-oriented site you go to are built for modern browsers only, but that's because all their visitors are using Firefox. Any good web designer still knows how to fix an IE6 margin-doubling bug, for example.
4. Flexibility -- um, it really is possible to design sites with good UI and flexible content. Would anyone here make the argument that Craigslist would have failed with proper whitespacing, appropriate font selections, and logical visual hierarchies? Those can all be accomplished with a single stylesheet.
5. Function -- this really is the point of design. Most good designers would tell you that. Design without utility is bad art. I love user interface design because I can build things that look good and work well. The two go hand-in-hand.
I may be reading too much into the comment that "in general, aesthetics simply don't matter." If that's really true, do you have a good explanation for Apple's success? How about Nike?