Bounded diameter conjecture for connected proper power graphs

For a finite group $G$, let $bdom? \mathcal{P}^*(G)$ denote its proper power graph, and suppose that this graph is connected. Bounded diameter conjecture. There exists a constant $c$ such that, for every finite group $G$ with connected proper power graph,

$$\operatorname{diam}(\mathcal{P}^*(G))\leq c.$$

The preceding results on proper power graphs of finite groups motivate this uniform boundedness question; the conjecture asserts that connected proper power graphs have diameters bounded independently of the group.