Positivity conjecture for quantizability of simple modules

Let $M$ be a simple module in the category under consideration, and call $M$ quantizable when its $t$-character specializes at $t=1$ to its $q$-character, namely

$$[M]_t|_{t=1}:={\operatorname{ev}}_{t=1}([M]_t)=\chi_q(M).$$

Positivity conjecture. Every simple module is quantizable. The supplied status evidence says that this conjecture is proved for reachable simple modules in affine types $C_n^{(1)}$, $F_4^{(1)}$, and $G_2^{(1)}$; no evidence of a proof for every simple module is supplied, so the universal statement remains open.