Conciseness conjecture for commutators of non-commutator words

Let $w=w(x_1,\dots,x_k)$ be a group-word, and let $G_w$ denote the set of all values of $w$ in a group $G$. The verbal subgroup $w(G)$ is the subgroup generated by $G_w$, and $w$ is concise if $w(G)$ is finite whenever $G_w$ is finite. Let $u_1,\dots,u_s$ be non-commutator words, with the variables in the different words disjoint as assumed for commutator words in the paper. Conciseness conjecture. The word

$$[u_1,\dots,u_s]$$

is concise whenever the words $u_1,\dots,u_s$ are non-commutator. This conjecture is a refinement of P. Hall's disproved conjecture that every word is concise; it is motivated by known conciseness results for non-commutator words, multilinear commutator words, Engel words in small weights, and commutators of two non-commutator words. The source presents this as a natural conjecture, and no resolution of this specific statement is given.