I think keyword density is an over-rated concept. Even with similar keyword densities one page may rank while another does not. And that’s true even if they have the same link profile. That in and of itself should show the (lack of) value of keyword density.
To explain how that concept works, consider a page that uses the exact same keywords at the start of the page title, at the start of their h1 tag, and in all their inbound anchor text. It may get filtered for being too closely aligned with the target keyword. Now imagine that the same page is redone, shifting word order is some spots, shifting singular to plural in some spots. Now the same page may not get filtered even if it has the same or similar keyword density.
Keyword density also has two toxic side effects. Some people write what ends up sounding like robotic copy. Others, in an attempt to increase keyword density, end up editing out important keyword modifiers and semantically related phrases, which not only lowers their traffic (since they took many relevant words off the page), but also makes their page look less like other top ranked pages.