I read them, but only after the résumé and application. If I think the person is worthwhile, I'll take the time to learn more about them via the cover letter.

The other time I might read a cover letter is if the application is horrendously bad, and that's solely for a private chuckle. (You don't want me reading your cover letter for that reason.)

I don't usually read them, but I (as an architect or team lead involved in the hiring process) am also not the target audience. The cover letter is the booster stage that gets your resume past the recruiter and into my inbox. A well-written cover letter shows that you can handle basic social niceties and give a good accounting of yourself to someone who isn't super-technical. That's a lot to try to do in three sentences.

When I'm writing cover letters I aim for under half a page in three short-ish paragraphs: one introducing myself, one talking about a relevant aspect or two in my work history, one tying that to the job posting itself. Unless the posting asks for more -- I've seen companies request that the cover letter talk about my favorite interview question, explain which of their values resonates most strongly with me, or even pick a side and argue on Postgres vs MySQL.

I've read several cover letters recently and in almost every case they raised red flags or seemed, as you say, disingenuous. This was partly from trying too hard to convey personality, and partly from a tendency toward banal tropes.

I think many people have an impulse to tell their whole story, which is a slog to read and sets up an interview in which we have little to learn. It's had me seriously reconsider what I might do in the application process in the future.

I've always been against cover letters in applying for much of the reasons you mentioned. However, I was recently in a conversation with several people in hiring manager positions who insisted a cover letter was necessary for them to consider someone's application. A cover letter, to them, showed the applicant cared enough about the position to read about the company and reference something specific in the cover letter, and also that they were capable of communicating clearly.
Unfortunately, as with most things, whether or not to write a cover letter depends on your audience. Based on some of the comments here, I'd advise people to write a concise, genuine cover letter. Genuine so it doesn't make them sound fake (as has been mentioned), and concise because it might not be read. It sounds like a not-bad cover letter won't hurt you, but not having a cover letter at all could.

My observation during my recent job search and from looking at resumes from applicants was that cover letters are useless. Most recruiting agencies and many larger direct employers use resume parsing software that ignores cover letters. The cover letter goes unseen. I have never seen a resume submitted by a recruiting agency that included a cover letter. At many companies that take resumes directly, HR strips off the letter and the hiring manager/team never sees them.

Resume review at the two best companies I've worked for were as follows:

1) The company was obscure, so by virtue of knowing about them you had an "in"

2) There were too many applicants so HR screened resumes and looked for pedigree primarily

After candidates pass to engineering for technical interviews I read resumes to see what questions are fair to ask; otherwise I don't care unless I see something fairly interesting.