The example you gave is the exception, not the rule. Sharing UX among these streaming sites is expected because they're completely replaceable, and you expect to churn through them as they shut down and pop up again somewhere else. Why would any of them want to change anything up if it might disappear in a week?

People like unique designs because those designs (ideally) exist to cater to the ever-so-slightly different needs, different things that different websites are meant to convey or do. It's not just about being pretty or looking not like everyone else, though some users and designers can mistake it for that.

Even something like video streaming can have lots of variations because there's so many different types of video content to serve. Optimizing for these needs will require making design choices, which will eventually compound in a unique UX. I enjoy websites that are fine-tuned for serving their purpose, and that manage to do so in a simple and performant way. Generic boilerplate designs can work fine on most 'average' websites, but going further requires putting more thought into it.