I've seen piano books (not mine) that bring the flat keys in with the sharp keys. I thought it might have to do with getting students a useable vocabulary earlier in the piece. Or else building confidence with the easier keys before moving on up. 100% certain whoever wrote the book has way more experience of students than I do.The organised way you presented the keys is the best way to go about this, although I would bring in F (1b) at the same time as 2#, along with relative minors.
I used the format I did because I thought it would be easier to understand the theory if I explained how the sharps work progressively in fifths and the flats work in fourths. There's a strong probability those posts will never become anyone's practice routine. That if the OP wanted to follow the exercise right through, he'd buy a book or get a teacher. Best I expected of my post is it'd help make the theory seem more accessible.