The process outlined in the post also isn't a path to writing a good cover letter. You don't want to just go over your resume again you want to either talk about things that wouldn't be there (e.x. why you want this job specifically, because your 100% applying because this is the unicorn job for you, not because you need money to feed yourself) or expanding on how something on your resume uniquely qualifies you (I worked on this project that's very similar to what your doing)
If it's lining up your resume to the job description (you want someone who can write Scala, I have used Scala in my past 3 jobs) a resume is a better format for that. But that's all the LLM has context to do.
Oh yeah, ideally you'd also tune your resume to the job too.