A self-starter is what the job description says when the company has not decided what the job is.
The term signals opportunity. What it describes is an absence: no onboarding structure, no defined objectives, no one who will explain what success looks like or when it has been achieved. The role exists because something needs doing. The company has outsourced the definition of that something to whoever accepts the position. This is presented as autonomy. The people who wrote the posting understand the distinction perfectly well.
The colleagues who have been there longer understand it too. They watched the last one navigate the same absence, and the one before that. There is no pleasure in it, particularly. It is more like recognition of a familiar sequence: initial confidence, a period of asking questions that have no answers, a quieter period, then the exit interview. The cycle is structural rather than malicious, which is in some ways worse.
“Self-starter” remains in the posting because it works. It selects for people willing to accept ambiguity as a feature. Those people tend to stay long enough to be useful. The ones who needed clarity leave before they cost the company very much. The template has not changed in years. There is no reason to.