Earlier quoted context omitted.
You don't need to demonstrate emotional attachment. You do need to demonstrate that you can solve the problems of the potential employer. People advertising for a job have a business problem to solve. If you can demonstrate that not only can you solve that problem but that you have solved similar problems for other businesses before, then you stand a greater chance of making it through to an interview.
You're right! Cover letters are all about demonstrating value. Cover letters are great for copywriters, marketers, and others whose primary output is prose for humans. In such cases, cover letters demonstrate competence for the job at hand. However, software engineering is not such a job. A cover letter showcasing a software engineer's ability to author vaguely reality-flavored prose and get past the HR drone doing t…
> I've literally never had a good experience with a company that wanted a cover letter.
To provide a counter point, for a recent contracting job, I got an interview with a cover letter only (no resume), and then the position.
I had responded to a 'we're hiring' link at the end of a technical blog post (linked to from HN). I wrote a brief email introducing myself and talking about the value I thought could bring to the company (with links to examples of prior, related work), and that led to follow up emails and an interview. I don't think it would have gone any further if I had just sent an email saying 'Please find my resume attached' and then sent a generic resume.