This question asks about Goethe as an essential starting point in context of two streams and worldviews, the materialistic mineral science and the spiritual science. Implicitly (and most interestingly) it also asks about the role of a life as Goethe's in a broader context of human development.
I will give a short direct answer to start with, and afterwards provide angles to look at for one's personal study and deepening.
The direct answer:
Rudolf Steiner positions Goethe as a representative of an impulse that is pivotal for humanity to connect to and engage with. He is a representative of several things ... of Goethean science as epistemology, but he also brought the theory of metamorphosis of plants, and colours, the Earth as a living being, etc . These are all about knowing life, the element of the etheric formative forces, so (referring to the four elements) beyond the element 'earth' but also about the element 'water' .. and this also relates to the faculty of imaginative cognition. Furthermore, he is a representative of the wave of german idealism (philosophy) and was also great poet and author (art). So we see the combination of philosophy, science and art .. with a new impulse that brings all this out in the open as cultural renewal.
Deepening the aspects of that statement:
First: about 'in the open' .. the current cultural age and the start in the 15th century saw a bifurcation of two streams: an overt of mineral science most well known, and a covert of rosecrucianism which had to live 'underground' in secret societies, use the veiled language of alchemy, etc. One should not forget about the inquisition, the index of the roman-catholic church, people being burned at the stake (see: Worldview wars#Middle ages). With Goethe this changed as he brought a counterweight to mineral science with an alternative epistemological and philosophical approach as foundational for spiritual science. There is a lecture where RS literally juxtaposes these two paths and describes this picture.
Secondly, to 'see' this more broadly .. Rudolf Steiner often sketches the polarity, opposition and radical bifurcation between the scientific approach represented by Bacon (1561-1626) and the one by Goethe (1749-1832), which in a way similarly maps to the polarity between Kant (1724-1804) and Hegel (1770-1831). To coin it rather black/white with shortcuts. Bacon 'torture nature and see how it reacts to experiments', Goethe 'observe phenomena of nature using the human soul, and see it living'. Hegel 'include the human as part of the whole' vs Kant. Steiner goes into this quite often, and also its consequences .. that mineral science is deadening and lacks the moral dimension, whereas moral ideals are essential for the future humanity. This shows it is not just about science but about the whole worldview.
As always there are many more angles to this, like:
- For the consciousness age, what is essential is to have the inside-out soul Parsifal attitude (Schema FMC00.380) fertilized by the spiritual, for which I usually refer to the metaphor of the semipermeable membrane - see notes to Schema FMC00.431. Man should ask questions and use the full human soul faculties, and not just intellectual thinking with the bandwidth filter of current senses. As we know this is an essential step for fructification by the Christ Impulse (see Schema FMC00.468 .. also Schema FMC00.438)
- This impulse fits into a stream where other Individualities could or should have contributed (re Plato-Schroer, Kaspar Hauser with Bismarck after the preparatory german idealism), and as not all of them did .. this is also what Steiner picked up and continued .. establishing a renewal of this impulse (along with others, not just generations of anthroposophists, eg see also descriptions about H. Grimm in this context).
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Steiner used Goethe as a symbol for all the above: he represents the epistemological approach of Goethean science, the union of philosophy-science-art with moral ideals and a science that includes the living. These are key if humanity wants to go beyond the mineral science of element 'earth' (and the grave consequences for the human soul of that worldview) to the element of life in nature ('water' or the etheric). It is a matter of escaping the materialistic worldview that is a dead-end street that will have catastrophic consequences for humanity ... and offering an alternative. So that is what Rudolf Steiner is pointing to with this simple statement of 'go back and start with Goethe', because we have to let go of much that is engrained by the dominant established cultural-scientific worldview, today even much more than a century ago.
To conclude, if to choose one picture to illustrate the above as part of 'the bigger picture', I would propose Schema FMC00.054A
For the second part of the question with the quote from the Kuerten book, I refer to the two sub-aspects on Impulses from waves of reincarnating souls#General that contain the answer. We can come back to this and discuss or deepen this in another thread if you want.
