For those readers who are skeptical whether this curriculum is really in widespread use, it definitely still is.
I have young kids and before listening to this podcast, my wife and I spent a bunch of time last Fall looking at schools for our eldest to start Kindergarten, because San Francisco's lottery system means there's no default school.
A lot of schools, even fancy private schools, used materials designed for this three cues reading curriculum. We were really puzzled why the reading curriculum featured stupid books where each page had a picture of a mouse and another object, and you were supposed to read "Mouse sees bear".
These books had two problems that were obvious to us as parents: You don't need to know how to read in order to appear to read the book (just be shown the pattern for what to say on each page), and the books are _incredibly boring_ -- even our 2-year-old wouldn't be interested in reading such a book. The teachers we talked to said things that in retrospect echo the marketing lines for this curriculum that you here about in this podcast.
We Googled why these stupid books are being used in schools at all, and found https://www.apmreports.org/episode/2019/08/22/whats-wrong-ho... (An earlier article the by the host of the Sold a Story podcast). I recommend the article for folks who want to read something on the topic, though the podcast is the result of her considerably deeper investigation into why this is happening, and I highly recommend it as well for those who have the time.
We ended up sending our daughter to a Montessori school; we picked it for several reasons, but one observation is that because they have their own philosophy about how to teach reading and writing, they're relatively resilient to this sort of fake "science" based fad.
(Other things we saw visiting schools that made me sad included plentiful posters about the CUBES math strategy, which felt like an algorithm for being able to produce the correct answer to a word problem without actually reading and understanding the words -- i.e. an adaptation of the math curriculum to a world where many children struggle to read).