  We examine the large-$g$ asymptotic Weil-Petersson volume formulas deduced in
the previous literature. The volume formulas have application to computing the
partition functions and the correlation functions in Jackiw-Teitelboim gravity.
We utilize two approaches to assess the validity of the formulas. The first
approach is to examine the asymptotic volume formulas from the perspective of
the Witten conjecture. If the volume formulas are correct, the generating
function of the intersection indices deduced from the asymptotic volume
formulas would satisfy constraints that are analogous to the Virasoro
constraints. We confirmed that the intersection indices computed from the
large-$g$ asymptotic volume formulas satisfy variants of the string and dilaton
equations. This implies that the generating function of the intersection
indices deduced from the asymptotic volume formulas indeed satisfies
constraints analogous to first two of the Virasoro constraints. As another
approach, we also examined the asymptotic volume formulas by studying the
behavior of the higher-order spectral form factors. Our analyses suggest that
the large-$g$ asymptotic Weil-Petersson volume formulas yield plausible
estimations.
