Headhunters are the cover letter though, and like to at least claim to employers that they've done some basic screening for fit beyond obtaining the CV. They're also rarely involved in the sort of hires with so many qualified applicants nobody needs to do anything to stand out
In general, my understanding has been that the résumé should be showing what you've done, learned, and can do, while the cover letter should tell why you'd be good at doing it there in particular. But I've seen job ads that had very specific things listed as expectations for cover letters, and I've seen stories from hiring managers who act exasperated that "no one" has these particular elements to their cover letters (or résumés), which were never communicated, and seem to just be that particular hiring manager's random expectations.
It would be great if there were some kind of standardized format for all of this information, and some assurance that companies that try to buck the standard will suffer for it, but we really don't have that.
Jobs are exchanging work for money. Asking more than that turns it into a cult.
I wonder if psycho employers think they are Jesus.
It's important information because if you have two candidates that are otherwise equal, and one applied to the position just because it's a job they qualify for but the other applied to the position because they're excited by the work or company, you'll go with the second one every time. Everyone will be happier for it.