The Verschiebung lower-bound conjecture for finite unipotent group schemes

Let $k$ be a field of positive characteristic, and let $G$ be a finite unipotent commutative group scheme over $k$. Let $V:G^{(p)}\longrightarrow G$ be the Verschiebung, and let $n_V(G)$ be the minimal integer $n\geq 1$ such that $V^n=0$.

Verschiebung lower-bound conjecture. The essential dimension of $G$ over $k$ satisfies

$$\operatorname{ed}_k G\geq n_V(G).$$

This is proposed in the paper as a generalization of Ledet's conjecture. The supplied text gives no evidence resolving it.