I am completely outside the industry and there is zero reason to pay attention to my analysis, but luckily such matters are no restriction on the internet!
Yeah, being “effective at reaching the target business” is the ultimate goal, but this goal is always understood to be present. I don’t think that advertising an ability to make beautiful websites is empty language, it is a description of how that goal (reaching target business) will be achieved. Yes, it it only part of the overall equation, but I suspect that many would consider it to be a powerful part, and also something easily expressed in an ad.
However, I guess there is a counterargument goes something like: if the importance of “beautiful” websites is widely accepted, then it too is a goal always understood to be present, and therefore any promise to deliver a “beautiful” website is just as useless as a promise to deliver a website “effective at reaching the target business” – people know you’re going to try to do this to begin with.

I think I may have just argued that ads are meaningless in general, which is totally not what I started out to do….

I think in the case of Happy Cog what they mean by this bit of uninspiring marketing is that they design sites that are excellent, successful, and visually captivating. Which is as close to the definition of Beautiful as a website can get.

Also, who can blame them for keeping their copy low key? It’s not like there’s a shortage of business coming their way.

The bulk of my client base wouldn’t know “beautiful design” even if they were beat about the head with it. They look for function. And I try to talk them out of more serious design sins – but I’m not always successful.

A lot of times there’s a huge gulf between what the designers see as exceptional design, and what the client wants…The hard part is selling the client on something they don’t really understand.