For better or worse, sunsets are just a social bridge. The value is, apparently, in sharing a moment with others. Both are ephemeral.
Sure you may appreciate the experience of watching a sunset live, but clearly the social sharing aspect may be more important to others.
Aside from sharing, we like to photograph things as some sort of time-space marker for ourselves, even if we never do anything with it. "This is memorable, so I should take a photo to affirm that." That's why everyone takes a goddamn photo of the Eiffel Tower.