I'm going to have to disagree with you on this one.
Most practitioners wont even come to an authentic realization of the preciousness of life and impermanence, let alone be prepared to fully and authentically engage in the practices of trekcho and togal.
Buddhism first came to the attention of the Western consciousness around the turn of the 19th century (1800AD). When missionaries, colonialists, merchants etc found India, Ceylon and so on. Initially the earliest European scholars mastered Pali and Sanskrit and translated the Theravada pitakas and some Mahayana sutras. Later came people like Max Muller who oversaw the mass translation of Sanskrit Buddhism (and Vedic Hinduism), and the Pali Text Society which oversaw the issuance of the entire Theravada tipitaka in English. In the early decades of the 20th century certain scholars and explorers reached Tibet and reported on the mysterious culture and religion they found; there arose the Theosophical movement, people like Blavatsky aligning themselves with the shamanistic/magiko-gnostic elements of Tibetan spirituality. Then we have figures like Jung engaging in comparitive investigation of Western psychology in relation to Buddhist ideas like the alaya consciousness, after-death experiences as outlined in the Tibetan Book of the Dead and so forth. With Huxley and Leary we have seen how conformitive consciousness is limited and the whole 1960s movement expanded the outlook on mind, together with the thinking of Camus, Satre, Hesse and so forth. Also in the 60s Conze translated the bulk of the Prajnaparamita literature and the first authentic Dzogchen communities sprung up in the West around the 1970s. The escalation of scholarly interest in the Mahayana since then has far outstripped the same in regard to Hinayana and today most of the most important Mahayana sutras are available in English, and many of the key tantras of the various levels, thanks to scholars like Vesna Wallace, David B. Gray, David Snellgrove, Alex Wayman, Gyurme Dorje and many others.
And now even many Dzogchen texts and commentaries by the original lineage holders of ancient times like Garab Dorje, Manjushrimitra, Jingpe Lingpa and Padmasambhava and Longchenpa and modern masters like Namkhai Norbu, Mipham, and Dudjom Rinpoche are readily available.
In addition, the relative politico-religious freedom and material prosperity in modern Western democracies means that these teachings can be taken up and disseminated freely and happily.
This is why the current age is an enviable one in the West where there is a unique and distinct opportunity for people to study the whole gamut of the Buddhist teaching and learn the highest way and realize enlightenment.
If people are missing all this like you say they are, then they were never going to get it anyway!
Anyway, there will always be nay-sayers in any era; there were at the time of Padmasambhava in Tibet, there were at the time of Tsongka pa; there were at the time of Nalanda and the time of the Buddha too, who say enlightenment is not a reality or the people are not ready for the teaching because of this or that.
To get back to original question, When is one ready for Dzogchen? The doctrinal standpoint is one is ready when one has understood and transcended the view of cause and effect, or pratityasamutpada, as being the definitive character of appearances.
The doctrine of cause and effect was taught by the Buddha to uproot mistaken notions about existence, and once he had done so the nirmanakayas like Garab Dorje and Padmasambhava came and explained the higher teaching which transcends cause and effect.