Desynthesis - Materia

[Covenant]

Much like the moblin that takes 5 materia and grants you a chance to get upgraded or similar materia, how about a "desynthesis" that takes Higher valued tiered materia and "cracks" it into smaller tiered materia. Examples
materia X > (2)materia IX
Materia IX > (2)materia VIII, and so on.

There is a chance to "lose" materia in process.

[Caitlinzulu]

WHY?????????

[Covenant]

im lazy, sometimes running out of lvl 3 or IV tier materia

[Jojoya]

I don't see them doing that when V, VII and IX are more valuable than VI, VIII and sometimes even X for DoL/DoH materia.

If it's IIIs and IVs you're worried about, just buy them from the MB. They're cheap (to the point it's not unusually to find them at/below sell to vendor price).