What I'm saying is that beauty in design doesn't come from slapping a facade onto something. It comes from a harmonious relationship between all the elements, adding up to something that solves the particular 'problem' of that site.

UI is a specialization within UX, the way databases are a specialization within Computer Science. CS deals more broadly in the constraints of memory, time, resources, etc. Databases deal with the same things, but through a specific lens.

UX deals with a set of constraints as well. The business needs, the user needs, etc. UI deals with a narrower subset of those constraints.

The fonts you choose, the colors you choose, the information density – if these are intentional choices based on your particular set of constraints, you'll end up with something elegant. That elegance is what makes something feel right.