Hafnia / Zirconia polymorphs as a function of T

[Useful nucleus]

The room temperature polymorph of hafnia and zirconia is the less symetric monoclinic, by heating both of them trasform to the more ordered tetragonal structure, by further heating they transform to the cubic flourite structure and eventually they melt.

To me it looks counter intuitive that they get more and more symmetric by heating up to the melting point! Any explanations or thoughts?

 

[Useful nucleus]

Let me explain more,
My undesrtanding is that the entorpy is proprtional to the degenracy or the number of accesible states. Also heating adds more entropy to the system.
However, the symmetry tends to reduce the degenracy which (to me) seems to contradict that the entropy of the cubic phase should be larger than the entropy of the monoclinic one.

Am I wrong in my argument?