As to that Sutta you mention (A. IV,159: ii,144-7): a bhikkhunī sends for the Ven. Ānanda Thera, being infatuated with him and hoping perhaps for sexual intercourse. The Ven. Ānanda understands the situation and gives her a suitable Dhamma-talk. He tells her (i) that this body is a product of food and that, depending on food, food is to be given up (a bhikkhu's body is made of food, but he must go on taking food to keep alive and practise the Dhamma if he wishes to give up food in the future by not being reborn); (ii) that this body is a product of craving and that, depending on craving, craving is to be given up (a bhikkhu, having been born on account of craving in his previous life, hears that so-and-so has become an arahat and, craving that for himself, sets to work to get it; and in course of time he succeeds, his success being, precisely, the giving up of all craving); (iii) the same with māna or conceit (the bhikkhu, hearing that so-and-so has become an arahat, thinks 'I'm as good as he is, and if he can do it, so can I', and sets to work; and in due course, prompted by conceit, he puts an end to conceit); (iv) that this body is a product of copulation, and that the Buddha has said that (for monks) copulation is absolutely not to be practised. In (ii), the bhikkhu craves for arahatship since he thinks in terms of 'I' or 'self' ('When shall I attain that?'), and all such thoughts contain bhavatanhā, though of course here there is no sensual craving (kāmatanhā). But anyone who thinks 'When shall I become an arahat?' is ipso facto failing to understand what it means to be an arahat (since being an arahat means not thinking in terms of 'I'). So, on account of his craving for arahatship, he sets out to get it. But, since he does not understand what arahatship is, he does not know what it is that he is seeking; and when, in due course, he does come to know what it is he is seeking, he has ipso facto found it (or at least the first installment of it). It is by making use of bhavatanhā that he gives up bhavatanhā (and a fortiori all other kinds of tanhā). I think that Sister Vajirā, in her last letter but one, says that she had not known what it was that she had been fighting against, but that she now saw that the solution had been staring her in the face all the time without her being able to see it. This describes the situation very well. It is because of bhavatanhā that, with the Buddha's help, we make an attempt to recognize bhavatanhā and succeed in doing so, thereby bringing bhavatanhā to an end.
I fully agree with you that the curtain came down on the drama too suddenly. I was hoping for a further letter but was disappointed. And when she was packed off there was no further chance of meeting her and filling in the gaps. But if in fact she really did cease to be a puthujjana (and I see no reason to doubt it), then we are perhaps fortunate in having as much as we do have in the way of a written record of an actual attainment of the magga (and probably also of the phala) as it took place. An account written afterwards from memory would not have the dramatic force of these letters which are so striking.
