The use cases listed in that pdf are revolving around compression, e.g. graph adjacency list is listed as one. I myself found the last use case listed as smelling interesting (colored range queries), but I would need to dig into the references on that one to see what's actually going on with that one and is it truly anything interesting.
I would be interested in things like what's the unique advantage wavelets trees have compared to e.g. stuffing roaring bitmaps or other kinds of bitmaps into a tree. The RRR has rank-and-select queries which I think roaring bitmap won't do, so that might tie into something. Maybe a problem where the wavelet tree is the only known efficient way to solve it, or maybe it is uniquely really easy to throw at some types of problems or something else.
Anyone know real-world examples of wavelet trees used somewhere? I got interested enough to dig a bit deeper but on the spot as I'm writing this comment, I'm not smart enough to immediately see do these things have killer applications in any niches.