Good design is actually a lot harder to notice than poor design, in part because good designs fit our needs so well that the design is invisible, serving us without drawing attention to itself. Bad design, on the other hand, screams out its inadequacies, making itself very noticeable.
Good web design is easy and enjoyable to interact with. Its purpose is to engage the average user in such a way as to evoke a positive emotional response. If you saw or interacted with a product or advertisement that left any impression other than negative, you made use of good web design.
If a person is distracted by the alignment of this or the color of that, they will totally miss what you're trying to say through design. They'll miss that your law firm is trustworthy, knowledgeable, and premium. More importantly, they'll miss why they should give their money and patronage to your firm and not some other attorney. If they're looking for legal services, they have a problem that needs to be solved. And the only difference between you and the law firm that lands the client is good web design and marketing. More often than not, the average person won't even know why they don't like a design. There are subtle psychological decisions made in good design.
While some web designs can be expressive and visually striking, that's not necessarily their prime objective. Good design decisions aren't based entirely on whimsy or ego but solid and proven principles. That's not to say that web design is not creative. I believe that working within a set of parameters and designing a solution that hits all the moving targets of good design takes some very clever strategic thinking.