Does It Matter Which Kid's Piano Book I Buy?
Does it matter which kid's piano book I buy? No. Any kid's piano book can be used to start piano lessons. But here's the problem. Unless that book is in the hands of a very good piano teacher, you may run into problems very quickly. For a teacher, you need Albert Einstein with the bedside manner of an affable Harvard doctor. In other words, it's not the kid's piano book, it's the teacher's delivery. Kids care less about what is being taught than who the teacher is. It is the teacher's personality that draws them to the material.
Use Child Psychology
Piano teachers would do well to take a course in child psychology rather than another master class with the Maestro. Even the best kids piano book is limited by how well it is presented to the child, and geared to the personality of the child. You could use no book at all.
Use No Set Method
Many kids need to learn piano visually, or by ear. You have to determine what the child can stand. Reading music is very exhausting because of the relentless detail. Even the most capable child needs a break from it. Veer off into the realm of pure music not found on a page. Some kids cannot bear to read music, and desire only to live in the realm of pure music not found on a page.
Too Much Effort For Most Teachers
This is a problem only insofar as the piano teacher must painstakingly spell out and show every single note, usually one at a time, to the kid. Most piano teachers refuse to do this. It's too hard. For the teacher, it's far easier to go page to page. Reading music isn't the be-all and end-all of piano study. In fact, you'll "end it all' if you insist on only reading music. Yet almost all piano teachers pursue this path because it is easiest for them. They go from page to page. And they insist you learn the way they learned, or get out.
Far Harder To Find The Child's Need
It is far more difficult for a piano teacher to try and figure out how to interest a child than to apply a single circumstance to all students. This is laziness personified, but you'll find something like it in nine out of ten piano studios. If your little Johnny really has a problem with the Bastien Book 1, it is usually utter boredom. There is really not much most piano teachers can do except brand him un-teachable. These inflexible teachers don't accept blame for anything. In reality, little Johnny could learn to play perfectly well if you were patient enough to figure out how to do it.
Page To Page
Going from page to page in a Bastien book is not going to excite any child I know, including little Johnny. I use Bastien every day, but in combination with two or three dozen other things. Have many arrows in your quiver: I look at the kid to see what tool is required today.