Solvability from the average element order threshold of $A_5$

Let $G$ be a finite group, and let $o(G)$ denote its average element order. Let $A_5$ be the alternating group on five letters.

The average-order solvability conjecture. If

$$o(G)<o(A_5),$$

then $G$ is solvable.

The conjecture is proposed by analogy with results for character degrees and conjugacy class sizes. The source gives no resolution status.