I don't know that my personal n=1 anecdote adds much to this discussion, but FWIW...
My mom taught me to read when I was young (pre kindergarten), but as far as I know she wasn't specifically trying to teach me to read. She just read to me a lot, where I could see the page she was reading from. Mostly she read me comic books. I loved the DC characters back then - Batman, Superman, Wonder Woman, Flash, Aquaman, Green Lantern, etc. and so she read me that stuff many many times. I mean, yeah, I had some of those "Little Golden Books" and stuff around as well, although I don't pointedly remember reading those the way I do the comic books. Anyway, she did all that and when I started kindergarten at 4 (due to being a summer baby) I was already reading. And then stayed well above my grade level on the reading tests all through school.
So I dunno. Maybe it was dumb luck that things worked out that way for me. Maybe there is a genetic element. Or maybe more than anything what mom conveyed to me was a passion for reading (she was a very avid reader herself). Maybe part of it was just that there were always plenty of books around the house and so reading felt like a very natural thing to do. Or maybe it was that whole Pizza Hut BOOK IT thing they had back in the day. Who knows?
In either case, I feel very fortunate in this regard, as reading has remained a big part of my life ever since, and still is to this day.
So the reason some kids seem to read with some instruction, even if it's not formal and super explicit, is that they have a good phonemic system. That is, they quickly understand that words are made up of smaller units (e.g. cat is /k/ + /a/ + /t/) and can manipulate them without much trouble. That ability is essential to map words efficiently in long term memory for effortlessly retrieval, which in turns creates a sight vocabulary (a large bank of words that are instantly recognized).
Kids with phonemic deficits, on the other hand, cannot efficiently develop a sight vocabulary. Even if they are taught phonics and can decode, that decoding is effortful and leaves little room for more complex tasks.
For what it's worth, a pivotal moment for keeping reading going after the lessons was when my partner picked up a comic book at a library event. For a few weeks after the end of the lessons, reading time had been traditional early readers and some of the books we'd previously read to them--even with us offering rewards, there had been ups and downs. As soon as kid started that comic, though, they were pushing right through our protests that it was bedtime, and chewing through the whole series. Luckily we managed to find another series to start before running out of the first one. As parents we can nudge or put stuff on the menu but but kid is pretty much in the driver's seat about what to read next.
In retrospect, of course! The kid just hadn't liked reading those books and things took off once we found stuff they liked. Best first readers are whatever your kid actually wants to read!