Neither the notation on the page or the sequence of progress will affect the tone/pitch and ensemble sound? That is in the hands of the ear of the director. The publishers are very good at providing a tool that will help students develop musicianship, but it is not within the book to reinforce these nuances that are so important to what we do.
Any method book will need additional resources...no one book does it all.
Search for outstanding beginner programs and ask what they use, and just as important, what they use and do in addition to the book that they are using. Also ask if they can provide their strategies/scope and sequence plan.
book does that. It's the teacher. All of what you mention is based on teaching characteristic sound/tone. You can't tune a noise and you can't get an ensemble sound if you don't have characteristic tone/sound/pitch that match and blend based on listening and good playing techniques. A book doesn't do that any of those things. You do.
I totally agree. I've taught at several schools and used what books I inherited. I wouldn't trash or treasure one book over all others. I finished my career with Essential Elements 2000. It was nice to use the same book over time and have it all memorized. Getting my nose out of the score and into the business of watching and helping kids learn was "essential" to their success.