It seems that most companies want to reach out to as many people as possible with their websites. With differing interests and needs it is, unfortunately, impossible to cater to everyone with your business, you know ... unless you're Walmart. Good designers will tell you to speak to your clientele specifically, or you won't be speaking to anyone. But, is it possible to still create lasting impressions about your company on anyone, even those who may not have a particular interest in your business? I think so.
People enjoy looking at shapes and pictures that are well placed and are in harmony with one another. This is true with almost all aspects of design. I hear people often comment about clothing as "I really like this, but it's just not me." You may also be able to recall picking out new home furnishings and thinking "I like this, but I don't see this fitting in my house."
People appreciate good design, even if it doesn't perfectly fit them.
I'd be willing to bet that it is perfectly plausible for one to like a site that (let's say) uses their least favorite color as an accent. That's because contrast is key when it comes to color. You don't want to overwhelm your site with color, but rather set up a pleasant environment, have great contrasts that create dynamics and provide accents that high-lite key information. Pleasantries are often established with less than preferable colors.
Content should be of utmost importance. It is the best thing a business owner can contribute to one's website. You should write with your clients in mind, but good content can be recognized by anyone. Books, short stories and play are appreciated by readers without any intrinsic interest in the subject. Anyone can appreciate and even like a well written website.
Even though all satisfied viewers may not be potential clients, they are all potential advocates. A positive impression can translate into free advertising through word of moth ... all based on the experience provided by a good design.