I don't have any discussion on the LLM factor of this conversation, but I'll weigh in on cover letters. As a hiring manager running a fully remote team with medium-low on the pay scale, I can tell you that any open position I post is inundated with 700+ resumes. This is after initial HR filtering. There is no way realistically for me to review all of these resumes, and cover letters I will just completely ignore. I basically draw arbitrary lines in the sand to reduce resume count below 100 (college degree, no unemployment gaps, at least 2 years exp at each job), and even then it feels like throwing darts to pick a reasonable amount of candidates to interview (10-15). And don't even get me started on the candidates that don't actually have any of the experience that is on their resume, or that are googling every question I ask, or are showing up on camera in sweat pants and a tank top.
I dread interviewing and will almost always just ask my network or coworkers for referrals because posting positions online seems such a terrible way to source candidates these days.