I have all the books mentioned in this thread 👓️ and plenty more 😁
Note that the OP spoke about books to "learn play the piano". So the Reblitz and Igrec books do not qualify. They do not say almost anything about how to play the piano. However they are highly recommended for anybody who wants to know how the piano works. If you want just one, I recommend the Mario Igrec book. He learned on the Reblitz book, so in a way it includes it 😆 and you need both only if you are a very specialized piano technician who wants to see how people do things (slightly) differently and/or if you are a hoarder as I am. If you already have the Reblitz or if price is an issue, having only that is fine too. However Mario is a (fantastic) pianist, so he has sprinkled the book with some pianistic gems which are prized if you play rather than (just) regulate the instrument. FWIW he is also the CEO of a Software Engineering firm he founded (not sure if you want to take that as "you can't make a living with pianos" or with "he's so good that he had plenty of spare time to fill").
Back to the topic of the OP, after having read, and followed a gazillion of books (I can post a list here, but do we really care?) I am now 100% convinced that (spoiler alert 😀)
You cannot learn to play the piano from books. REALLY!! You need a good teacher
How do I know? I've done it myself and I've seen it in practice with me, my daughter and a couple of friends . The most important word in the spoiler above is GOOD. If your teacher is not good, than a book could be even better. And note that good teacher does not necessarily mean good player
QuasiUnaFantasia Additionally, it seems to be the favourite pastime for piano book authors to pour ridicule and venom over their fellow piano book authors, which I find disgraceful.
I had the exact same experience and found it disgraceful too. In fact I also had the opportunity to speak with one of such authors and they felt offended when I said that what they were suggesting I read was similar in another book and that he could read that to check if it was really so or I was misunderstanding and possibly he could further improve his suggestions which I thought were very good.
But if one can "read behind it" and most important see below the apparent differences and find the underlying similarities in my opinion one will get a deeper understanding of the field. That said, I reiterate the spoiler above and add that learning to play pianos from books is like being a distinct marques who would not ever touch a saw and despise dust and especially sawdust, but knows all the intricacies of woodworking because he studied them.
: not a representative sample I know. But at least I could say that is the most likely result given sample size