Horribly designed sites can dominate old markets too. Amazon is the perfect example of why design doesn't matter. Likewise Craigslist and eBay... the list goes on and on. It's all about marketing and luck.
That only applies when there is no competition. Look at cars and firearms, for example. Pretty crucial items when they are needed but design is still at the forefront when it comes to making a choice.
Yeah, it totally depends where your business hits on the Maslows' Hierarchy of Needs.
If what your business provides is a basic need of somebody, a terrible UI/UX wouldn't stop the guy to use your website and get his job done. For example, look at many of the University websites.