Well I didn't get any music theory until the third for fourth year. And I don't think it did anything for me even then. What the names of the notes are, what sharps and flats are, what a key signature is and how do you count rhythmically to make the notes come out even. That was about it theorywise for three years.
By contrast, I got a lot of exercises. Five finger Schmitt exercises out of the G. Schirmer book, I did all of those in the book. Did a lot to strengthen my fourth and fifth fingers, how to play the five fingers in any order, whatever. Then the second and third year, Edna Mae Berman exercise books. There was something new to learn every week.
The there were the John W. Schaum books. Pre, 1,2. The pieces were boring as **** but that doesn't mean I could play them perfectly without a weeks practice. Sometimes more than a week. I did book 3,4,5 then branched off to pieces my teacher bought individually or in bound books. Everybody's Favorite Series Piano Pieces for the Young Student was my favorite, I still play pieces I learned in there. That was AMSCO music company #80. I was getting more fun pieces from the time of book 2, but the supplement pieces took me weeks to learn for recital.
Thousands of kids learned on these books. I still see them in the store ( not schmitt, it is on the internet only). I don't see any reason to jam them all in one new book except extreme third world poverty. And very little theory is needed, IMHO, unless the kid needs to play gigs right away like that replacement singer for Journey did, to feed himself.
I found one other book of pieces for the young student (2nd or 3rd year) at a charity resale shop last year that has some really fun stuff in it. Masterpieces of PIano Music, Carl Fischer pub, Albert Weir Ed. O3619.
And of course there is the hymnal if you are a Christian. there are pieces in there that are first grade level, but you have to figure that out for yourself.