Why should that be the case? Can you point to sources where you read that? In my experience, CHAMP clearly has advantages over HAMT in this scenario.
To answer your questions about using vectors of coordinates of keys: it depends on the design implementation of the vector's hash code, regardless if you use HAMT or CHAMP.
Using collections as keys in other collections is in general a performance sensitive subject. The available HAMT implementations in Clojure and Scala fail to deliver here.
The case study in Chapter 3.7 nests hash-sets into hash-sets (i.e., Set.Immutable<Set.Immutable<K>> sets). The CHAMP implementation yields minimal speedups of ~10x over Clojure and Scala due to the way it calculates and incrementally updates the collection's hash code.
Let's say that I were to use a vector of coordinates as the key to something in a map. Would CHAMP still vastly outperform HAMT?