What's the purpose of AN 2.61?

What could be the purpose of the Buddha teaching AN 2.61 below? Why is this relevant? How is this useful?

Without knowing, i assume that Samana Johanns answer is an accurate description of the views from buddhas time. It may explain the original purpose, relevance and usefulness of the sutta. Provided that we avoid getting caught in semantics (nimitta), the underlying meaning goes beyond attributes such as gender, for instance.

If one believes that anicca and anatta are true, it follows that norms and values aren't consistent between ages, persons or societies.

Two possible exceptions to the above could be compassion (karuna) and joy for others (mudita); two of the four brahmaviharas, which are claimed to be "timeless beautiful mental factors" (appamanna sobhana cetasikas), and therefore unbound to a specific person, era or location.

https://www.wisdomlib.org/definition/appamanna

I'm quite likely mistaken -- I'm not a scholar -- but when I read...

Mendicants, these two are worthy of a monument. What two? The Realized One, the perfected one, the fully awakened Buddha; and the wheel-turning monarch. These are the two who are worthy of a monument."

...then I imagine that the text might have been added a little late: i.e. at a time when people had become interested in what Buddhism had to say about the State and the Monarch and Society.

So -- though other answers might explain that's a useful or a skilful teaching -- I guess it's possible it might be similar to this answer.

And the observation in question is not my experience of all women -- I understand it to be true sometimes but not always, so occasionally but not generally.

When I say this I'm not by the way trying to imply that promiscuous sex associated with modern contraception is the new normal -- but my social experience of "females" is in and of societies where women have the same education as men, go to the same schools, learn to read and so on, which is relatively recent (i.e. maybe only in the last 100 years or so). People are individuals, I'm not sure it's sensible to generalise about differences in what people want, and suspect that many "generalisations" of this sort may be socially conditioned and/or stereotypes.

This didn't answer your question though, i.e. "what could be the purpose"? As for the "purpose" of the teaching I thought that Samana Johann's answer seemed plausible.

I won't accept my own answer here, but just to share.

This verse from the Rhinoceros Sutta holds the answer:

There is sporting (flirting) & love
in the midst of companions,
& abundant fondness for offspring.
(While) feeling disgust
at the prospect of parting
from those who'd be dear,
wander alone like a rhinoceros.

It exhorts those aspiring towards enlightenment (especially those interested in the monastic life) to flee from ignoble companions who are hungry for romance, sex and procreation.

Also from Iti 109:

This was said by the Blessed One, said by the Arahant, so I have heard: "Suppose a man was being carried along by the flow of a river, lovely & alluring. And then another man with good eyesight, standing on the bank, on seeing him would say: 'My good man, even though you are being carried along by the flow of a river, lovely & alluring, further down from here is a pool with waves & whirlpools, with monsters & demons. On reaching that pool you will suffer death or death-like pain.' Then the first man, on hearing the words of the second man, would make an effort with his hands & feet to go against the flow.

"I have given you this simile to illustrate a meaning. The meaning is this: the flow of the river stands for craving. Lovely & alluring stands for the six internal sense-media. The pool further down stands for the five lower fetters. The waves stand for anger & distress. The whirlpools stand for the five strings of sensuality. The monsters & demons stand for the opposite sex. Against the flow stands for renunciation. Making an effort with hands & feet stands for the arousing of persistence. The man with good eyesight standing on the bank stands for the Tathagata, worthy & rightly self-awakened."

I suppose "to die without getting enough" is a colloquial expression for being insatiable, indefatigable.

This is an emphatic way of saying that women have a strong instinctual desire to bear children. If you polled a big enough sample of women I suspect majority would say they like to have children, enjoy having children, and many would say they'd want to have more then one child if allowed by the living circumstances.

The point of this in context of Buddha's teaching is that samsara has built-in mechanisms for self-continuation. Natural phenomena have innate tendency to proliferate, to continue, to support their kin, to procreate.

Left unchecked, the stream of samsara rolls forward endlessly regenerating ignorance, confusion, desire, suffering, and desire to escape suffering. It is the ignorant pursuit of this desire is what supports the stream's momentum to roll on and on.