"By 13 both girls and boys have arrived at puberty and are both coursing with the hormones at levels close to the adult sex drive ( albeit higher ) AND have fully functional reproductive organs. For any society with a single step into adulthood; this is it. Only a culture where your Bat Mitzvah and your voting rights are separated by years can see it otherwise. But why?

What's missing at 13 but present at 18 is the ability to out-punch Dad when he tries to ground you.

We are also the only species whose muscular build at the age of sexual maturity is years behind that required to dislodge the Alpha Male from controlling access to the harem.

This is why, as soon as sexual maturity ceased being the only pertinant issue, we headed down the path where ones ability in fisticuffs determines what is ethical and moral."

Um. Plenty of animal species have sexually mature young who are involuntarily celibate.
Obviously there must be an adequate safety margin between the replacement breeding success, and the breeding capacity under favourable conditions (replacing losses or settling new habitat).
One density-dependent feedback mechanism is of course mortality, of young and adults, due to hunger and infectious illnesses. But it is not the only one.
There are many animals who under unfavourable conditions for breeding desist from trying and try to survive to better times, rather than try and fail in breeding. And in a population in marginal condition, there is often a significant fraction of adults who are sexually mature and might breed under better conditions, but don´t under the present conditions. Along with a fraction of adults who do breed.

Notably among the polygynous animals, breeding is often limited to a small fraction of alpha males who keep the beta males involuntarily celibate. Where these beta males are adult, sexually mature, perfectly capable of breeding if alpha males disappeared.

And although males can produce more offspring than females, females must also be able to produce more than their replacement. And under conditions where they cannot, beta females often also do not breed.

And who are the alpha and beta males? Well, in many species the adults do continue to grow stronger after sexual maturity, and the eventual alpha males and alpha females are beta males and females for an extended time in their youth... unless the alpha position is vacated by death or migration, and they can become alpha at an early age.

The question is - how should humans distribute breeding opportunities, and involuntary celibacy?