Mixing in rocks are a thematic element for the form with it being implied to be related but the official word is not mandatory.
Part of this is to maintain that Amazing is supposed to be a special miracle and not something Shouma can access freely that has comparable performance to the 100 Gochizo Over/Master.

Imagine you're John Toei and you're approached with a concept for a female-led hero series, that would not align with Precure's tone due to being more sci-fi and action oriented.
Would you
>try and staple it onto Rider
>simply make it its own thing to see if it works and let it be more aligned with the demographic who want superhero stuff with a female lead