Yes, but like every tool, it applies best to certain situations/problems.

If teamed up with other little algorithms and other concepts, the range of situations to which it applies can be extended.

Most math teachers don't take algebra and retroactively apply it to arithmetic for anything other than demonstration/proof purposes. They could dedicate some class time and homework to making the students practice arithmetic problems that, when leveraging certain algebraic concepts (like perfect square binomial/trinomial forms, like difference of squares, etc) are convenient to mentally calculate.