Earlier quoted context omitted.
Mine's not a cover letter in the usual sense but that's the closest analogy I can think of... I just write an email saying those three things and links to my stuff.
Right. The separate full blown cover letter is dead. We just put a short text in the initial email to go along the resume. That's also what I do and recommend.
Out of curiosity, in which country are you? AFAIK, here in Australia, not having a cover letter would pretty much prevent you from getting a job.