I recently saw a talk where the speaker was endorsing construction grammar (which type, I’m not sure) and in particular, a view of language as “constructions all the way down”. On the contrary: nothing in nature is all the way down.
Consider the material world, in many things can be described as particles: discrete, bounded entities which occupy positions in space and which can interact with other particles. And indeed, some particles are made up of other particles: solids contain molecules, which contain atoms, which contain subatomic particles, which are made up of fermions and bosons. But at some point, this really does break down: electrons, fermions, and bosons are not known to be made of smaller particles.
I take this to be an property of the natural world: many natural types are recursive, but the recursion must ultimately terminate.
The same is true for constructions. Certainly we can imagine a theory of constructions where larger constructions contain smaller ones, but when we get to atomic units that non-construction-sympathetic grammarians recognize —phonemic features, syntactic heads, etc.—we eventually have to stop subdividing, and the recursion terminates. One could define, say, terminals as syntactic constructions, but one cannot do so if a essential property of constructions is that they are constructed from smaller parts, since terminals are not so constructed in any relevant sense. This weaker sense of “all the way down” is a property common to any recursively defined data structure, including, say, the standard definition of context-free grammars and the constituency trees they build; it is nothing special about construction grammar as a discipline.