"Hit 1-2% keyword density and you're optimized."
No. Density is a tool from the era of keyword stuffing, and it's measuring an answer to a question Google stopped asking.
The comparison people should run: density checkers versus term-coverage tools (TF-IDF, or the Clearscope/Surfer family). Density asks "how many times did you repeat the exact phrase?" — a metric you can game and Google can ignore. Term-coverage asks "does your page mention the related terms that top pages on this topic all mention?" — entities, subtopics, the vocabulary of the subject.
That second question is closer to how the algorithm actually models relevance. Not "loan loan loan," but "loan, APR, collateral, amortization, origination fee" — the words a real article on the subject can't avoid.
Use density for one thing only: catching accidental over-repetition that reads badly. Use coverage tools for actual on-page topic-fit.
(That density study you keep quoting found a "correlation" of 0.0-something. That's not a correlation. That's noise with a percent sign.)
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"Hit 1-2% keyword density and you're optimized."
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