A far as design itself goes I'd say for most business it is one of the least important elements to a site, take a look at sites like ebay or google they look pretty awful/basic but are highly effective due to ease of use, fast load time etc. With ebay I'd say it is designed deliberately to look cheap. Would spent money on a dozen other things before the look of a site. I'd say the time when it is important is for sites selling luxury goods/expensive brand etc but that is a a limited number of businesses.
Design is not simply decoration. Each of the sites you have mentioned Snoopy would have been deliberately designed that way (as you have mentioned with ebay). There would have been a lot of thought about the type of users and usability of the site and I'm sure the design would have been a priority in these considerations.
I would change the discussion to say 'decoration' and 'embellishments' are of little importance to many businesses. It is more important to optimise the 'design' for usability and CTA. Once you have a strong design you can then add decoration to add visual interest, but it's not overly important (unless relevant to your target market, as might be the case with luxury goods/expensive brands).