I'm not qualified in hair biology - I'm just an amateur like just about everyone else on this forum.
Anyway, I've attached a paper by El-Domyati et al. They show that follicles are sometimes destroyed in A.G.A, but this is rare and only seen in old people with advanced balding.
But A.G.A becomes hard to reverse very early.
Now, if you compare genes for different traits related to hair growth -- beard thickness, unibrow, male pattern baldness, eyebrow thickness, and alopecia areata -- the genes associated with each are very similar, except for alopecia areata which is a clear outlier (involving mostly immunity-related genes). Of the 50 genetic loci associated with unibrows, 21 are also associated with A.G.A (42 percent). Eyebrow thickness shares 6 out of 10 (60 percent) with A.G.A. Beard thickness shares 3 out of 8 (37.5 percent). These genes are mostly members of major HF developmental pathways (Wnt, EDA, Shh, BMP, etc.) or transcription factors that control members of those pathways (Sox2, Runx1, Trps1, Blimp1, etc.). The outlier, alopecia areata, shares 0 out of 14 with A.G.A.
In other words, the genes determining whether you have short unpigmented vellus hair or long dark terminal hair between your eyes overlap heavily with the genes that determine whether you have short unpigmented vellus hair or long dark terminal hair on your temples. Or the same over a wider or narrower region of skin above your eyes, and so on. Given the tremendous overlap, sex hormones might influence hair growth by modulating the key developmental pathways (Wnt, EDA, Shh, BMP, etc.) and the transcription factors that control these pathways.
So I suspect the answer to "Why are androgens required for progression of A.G.A but not for maintaining miniaturization of affected hairs?" is probably similar to the answer to "Why are androgens required for development of terminal facial hair but not their maintenance?" And the answer to "Why is it so hard to turn A.G.A-affected vellus hairs terminal again?" is probably similar to "Why is it so hard to grow terminal hair all over my forehead?" I don't know the answers to these questions.
Note: Genetic loci with p < 1e-5 counted for A.G.A.