Plant medicine is a recent English phrase and it groups traditions that have no historical relationship to each other. Amazonian ayahuasca practice, Mesoamerican peyote and mushroom ceremony, the West and Central African use of iboga, and the Siberian complexes around Amanita muscaria arose separately, out of the plants each region actually had, and answer to different cosmologies. Reading them as one worldwide practice with local variants gets the history backwards.
The convergence people notice is real but it is a convergence of problem rather than of descent. Any tradition that gives a powerful psychoactive plant a religious role has to solve the same handful of difficulties: who is allowed to administer it, how the person is prepared, how the experience is steered while it is happening, and how what was seen is brought back into ordinary life. Preparation regimes, a trained specialist, controlled sound and a receiving community are the recurring answers, and they recur because the problem recurs.
The label also carries a therapeutic implication its subjects mostly do not. Very few of these traditions describe what they do as medicine in the sense a clinic would recognise. The Amazonian vegetalista speaks of plants as teachers with names and diets; Bwiti describes an encounter with the ancestors. Those are not clumsy statements of a pharmacological claim, and translating them into one loses the content. The atlas keeps the phrase because readers search for it, and records underneath it what each tradition says in its own terms.