Conjecture on powers of the Jensen–Shannon divergence

Let $P$ and $Q$ be probability distributions, and let $D_{JS}(P,Q)$ denote their classical Jensen–Shannon divergence. For $\alpha\in(1/2,1)$, consider the powered divergence $[D_{JS}(P,Q)]^\alpha$.

Conjecture on powers of the Jensen–Shannon divergence. The quantity $[D_{JS}(P,Q)]^\alpha$ is not a metric for $1/2<\alpha<1$.

The result would complete the classification established in the paper: the powered Jensen–Shannon divergence is a metric for $\alpha\in(0,1/2]$ and is not a metric for $\alpha\geq1$. Counterexamples are given for some subintervals of $u\in(0,1)$, depending on $\alpha$, but the assertion for the full interval $\alpha\in(1/2,1)$ remains open.