Why doesn't XeF6 displace oxygen from water?

Consider the following reactions (unbalanced):


$$
\begin{align}
\ce{XeF2 + H2O &→ Xe + HF + O2} \tag{a} \\
\ce{XeF4 + H2O &→ XeO3 + Xe + O2 + HF} \tag{b} \\
\ce{XeF6 + H2O &→ XeO3 + HF} \tag{c}
\end{align}
$$


Considering that the oxidizing power order of the xenon fluorides is $\ce{XeF6} > \ce{XeF4} > \ce{XeF2},$ I don't understand why $\ce{XeF6}$ is unable to oxidize $\ce{O^2-}$ (in water) to $\ce{O2}.$ $\ce{XeF2}$ and $\ce{XeF4}$ are able to achieve this (rather difficult) oxidation, but $\ce{XeF6}$ is unable despite having greater oxidizing power.


*Note*: I have a primitive understanding on this topic and a deep and elaborate explanation will be appreciated. Also, an explanation of the reasoning behind each individual reaction ( for example, why only $\ce{XeF4}$ disproportionates?) will be even better.


