Earlier quoted context omitted.
Well, it works both ways. You might send out 20 resumes. As a hiring manager - especially when using a "no filter" approach like posting on here (keep in mind that IME people posting jobs on Hacker News are more likely doing "guerilla hiring" and circumvent their HR departments) - I easily get 100+ resumes, and I don't have days to spend trawling through them. I think it was rands of randsinrepose who mentioned befor…
Do you have any data to suggest your approach works better than random selection? A lot of hiring managers seem to admit to not bothering to read cover letters. I diligently entered cover letter and resume information into a spreadsheet when hiring, and to be perfectly honest, the only correlation I could find between cover letter + resume and interview results was resume length.
What I have is interviewing lots and lots of people over a couple of decades, first contributing to hiring decisions and eventually making them myself. As developers you see patterns emerge and you start making use of them. For a halfway efficient review process you have to make a first pass over the resume submissions and whittle the pile down to a manageable size quickly, making use of patterns spotted in the past.
In that respect, my experience tells me that "no cover email at all" = "shotgunned resume to every job listing" = "not a good fit". That might not always be the case, but it's an 80/20 rule. Yes, I'll potentially overlook a couple of qualified candidates, but I'm probably already doing this after work instead of spending time with my family because I've decided to essentially circumvent the HR department.
Part of the cover letter conundrum is that if you come in through the front door (ie, the official job listing curated by HR), your resume is likely landing in some HR system and the hiring manager might not even see it. In that case, it's a total waste of effort.
If you're coming in through the "back door", say, via a post here on Hacker News, there is a good chance that your first contact is the actual hiring manager. She or he will probably at least skim your cover email.