It's very easy to think up balanced reactions that are completely nonsensical and the reason for that is hidden deep in quantum realm.

It is, but this will have to wait until late high school, when kids are old enough for matrices and complex numbers and Dirac equation and the origin of 2x^2 (2, 8, 18, 32 — the electron shells etc). You still can have meaningful and useful exercises meanwhile.

Given a reaction, you can balance it with fairly simple math.

However, if you want intuition as to how to create a new reaction or a novel molecule, simple math really isn't enough.