  In 2018, Kahle and Stump raised the following problem: identify sequences of
finite Coxeter groups $W_n$ for which the two-sided descent statistics on a
uniform random element of $W_n$ is asymptotically normal. Recently, Br\"uck and
R\"ottger provided an almost-complete answer, assuming some regularity
condition on the sequence $W_n$. In this note, we provide a shorter proof of
their result, which does not require any regularity condition. The main new
proof ingredient is the use of the second Wasserstein distance on probability
distributions, based on the work of Mallows (1972).
