Perhaps a minority opinion but I think the strength of the goth trope in a character is so good because it allows for an immediate design impact while also giving a reliable and sensible reasoning for new plot points within the story. And while familiar after a while the familiarity becomes something enjoyable within itself.
When I see a character like this I know more or less what to expect and instead of it becoming predictable it becomes welcome. Often these characters are used to juxtapose or create drama with other characters and so are natural centers of the story while so clearly being averse to it as characters. Attention is what they abhor but what they so often get. Which feeds so perfectly into the mindset of their trope.
And really I think there is a universal kind of satisfaction in the ideology of such characters. The dreary nature of their outlook on things, whether it is energetically done or mopey is intrinsically related to the human condition and so while it is extremely morose it is also rather easy to find it somewhat comedic. And so these characters bring out that most ancient of ideas. When I consider this trope done well it reminds me of the laughing skulls monks would keep to remind themselves of death. These characters often embody that mantra and it is one that can be understood by any person. Giving a clear strength to such characters even when done poorly.
As watchers and voyeurs the morose and the frightening are what we so often gravitate towards, as they fill us with the strongest of emotions. The goth character wields these concepts and forces them upon the narrative, allowing for not only enjoyable storytelling but relateable interactions as well. Because who doesn't think about death every now and then?