I wonder if anyone really reads the letters of recommendation.
I've served for about 15 years on my (top-10 US computer science) department's faculty recruiting committee, including three years as its chair.
Yes, we really do read recommendation letters. In detail.
We also compare multiple letters written for the same applicant. Letters that all cover the same strengths are suspicious, especially if the same list of strengths appears in the applicant's research statement. Letters from different authors that contain common turns of phrase are deeply suspicious, especially if those turns of phrase also appear in the applicant's research statement.
We also directly compare multiple recommendation letters written (at least ostensibly) by the same recommender. If someone writes a significantly stronger letter for applicant X than for applicant Y, we are generally more likely to interview applicant X. Letters (ostensibly) from the same author with significantly different writing styles are deeply suspicious.
(On the other hand, if we were convinced by a strong letter to interview someone a few years ago, and that interview out to be a disaster, we're much less likely to trust a new letter from the same recommender this year. Similarly, if someone writes "This is the strongest student in Area Z in the last five years" every year, we don't believe them.)
We also look for evidence of the (ostensible) author's expertise in every letter, not as an expert researcher, but as someone who understands the faculty job market better than the applicant. We prefer letters that offer direct, well-informed comparisons between the applicant and other researchers in the same field, past and present, at the same career stage. (But again, multiple letters offering the same comparisons are suspect.)
We also occassionally contact references directly to clarify points raised in their letters.
Any suspicion that a recommendation letter was not written personally by the person who signed it will almost certainly kill the application. It will also undermine any other letters "written" by the same author, and possibly other applications from the applicant's department (or at least their research group/lab). Applicant-written letters risk the professional reputation of the applicant, the ostensible author, and anyone else for whom the ostensible author is a reference.
professors/PIs do not have time to write such letters
Nonsense. Writing recommendation letters is a professional duty.
How should I write the drafts of three different letters of recommendations for myself
You shouldn't. You should provide your references with all your other application materials, including your research statement, which already spells out your judgement of your research record. You may want to provide bullet lists of accomplishments that don't fit into your statements. But you do not have the necessary expertise to write an effective recommendation letter yourself.