Regarding your claim about that paper being cited by papers in top journals, I checked the first five pages of citations in Google Scholar for combinatorics and probability journal papers.

It's cited once in an offhand way in the concluding discussion of "The Cycle Structure of Random Permutations." No categorical concepts are used there. Ditto for the "Independent process approximations" paper (except now cited in the introduction). Another one-sentence mention in the context of background literature appears in "Tree-valued Markov chains derived from Galton-Watson processes." Same for "A Combinatorial Proof of the Multivariable Lagrange Inversion Formula" and "Bijections for Cayley Trees, Spanning Trees, and Their g-Analogues."

There's a one-sentence mention with actual (slight) mathematical content in "Limit Distributions and Random Trees Derived from the Birthday Problem with Unequal Probabilities." But you don't need categories to prove the bijection they're referring to, from what I understand.

In none of these instances is the work used in a substantive fashion, and unless I missed something no paper features the word "category." It's getting cited because authors have a duty to survey any potentially related background literature.

(On page 6 I found "Commutative combinatorial Hopf algebras," which does use a functor form that paper. It was published in a journal that is decent, but very far from the top.)

So, I think we can reject the notion that Joyal's paper has seriously influenced the fields of combinatorics or probability.

I'm sorry to harp on this, but I see claims like yours about the importance of category theory thrown around a lot on here, and often I feel that they're clearly wrong. So I thought it would be good to provide some details this time around.