These days you need absolutely every edge. But do taylor it to the specific job application, and keep it short: nobody likes wasting time reading about irrelevant stuff.
Yeah I know, these days you are sending out about 100 applications a day, and tailoring a resume and a cover letter for each one is tedious. But unless the filters see the keywords in your resume, and unless your cover letter shows how your skills are just a perfect match to the job, you are sending those applications in vain.
All I really know is from my experience interviewing and hiring people. For me, cover letters are incredibly important and I absolutely read them.
The resume/CV gives the "what". What has the applicant done before? What is their skillset? etc. The point of the cover letter is to give the "why". Why is the applicant interested in this position specifically? Does the applicant understand what the company does? What interests or skills do they have that applies to this and that may not be apparent in the CV? That sort of thing. The cover letter is, basically, the applicant's sales pitch.
Cover letters should be tailored for the company and position you're applying to. A "blanket" cover letter isn't likely to contain the information I'm looking for.
For what it's worth, I always spend the time to craft a good cover letter specific to every position I apply to. Maybe it gets ignored, maybe not, but it does no harm and may help. I'll take every possible edge I can get.