When considering the rationale behind this, I personally find it helpful to look behind the scenes. As expanded upon by Maku in this lovingly crafted google doc: Original Bionicle Ideas, Revised and Expanded Edition - Google Docs
When Alastair Swinnerton, one of the brilliant co-creators of the franchise, and seemingly the foundation for many of the ideas that made Bionicle what it is, was originally envisioning the Toa, it was a simple four classical western elements: fire, water, earth, air. However, he was then informed that Lego had six product lines, so he would need six elements! Which necessitated new elements.
I imagine in the interests of not straying too far from the original intentions of his idea, the seemingly out-of-place elements of ice and stone were born. Which, despite all the headaches it creates, was probably for the best. Imagining the Toa Mata without Kopaka and Pohatu is like imagining the original trilogy cast without Han and Chewie.