Why the metric survives despite being obsolete
Keyword density persists because it is easy to compute and produces a number, and a number feels like a target. Every SEO tool reports it, which keeps it in circulation long after the systems it modelled were replaced.
It was a reasonable proxy in 1998, when relevance was largely term frequency. It stopped being one when retrieval moved to embeddings and entity resolution, which is why no current Google documentation mentions a target density and why writing to one produces text that reads as written for a machine.
The only version still worth checking: is the subject mentioned at all, and has it been repeated to the point of awkwardness? Both are answerable by reading the page aloud, which is a better instrument than the percentage.