For a woman's body in general, this is sometimes catastrophic. All doctors say that the biological time for a woman to conceive a healthy child is before the age of 25. What kind of study or career can she have then? Especially if she wants to have time to find a good husband and give birth to more than one child before 25.
This quote shows exactly the problem with the reasoning. You paint a very modern scheme, but judge it by antiquated social structures, and not even from the kind of societies that primitive humans would have had. Pair bonding is not necessarily as strong in hunter gatherer communities, if only that for a long time (on evolutionary scales) the relation between sex and delivering a child 9 months later was not as clear.
And anyway, you could solve this by implementing decent childcare and a living wage for graduate students (for single or both partners regardless of sex) right now for a lot less than all the futuristic nonsense.
Alexander the Great died at the age of ~32, having already conquered a large number of ancient states.
Jesus Christ died at the age of ~33, having become wise enough to change history for the next 2000 years and more.
Alexander's died of illness, Jesus Christ was not a natural death, moreover both are not related to hunter-gather societies.
You missed my favourite, Abraham died at the blessed age of 50. Nowadays that would be considered cursed.
Anthropologists say that the human body in general is originally designed for an maximum 40 years.
"designed"? You mean evolved?
Anyway. I'm no anthropologist nor genetics expert, but got a bit of biology and genetics as part of my chemistry studies.
Some parts of the body start to reproduce more slowly with middle age, but that doesn't mean that that middle age period is a hard maximum. IIRC the anthropologist view was that elders in social structures can help their offspring with their (first?) children, and function as longer memory for the tribe (e.g. when migrating). This has been shown to be the case in great apes, while starting to lower the metabolism eases drain on resources for the group/tribe.
Also, that doesn't mean that those human matriarchs(*) would no longer be able to reproduce at that age. In a natural (hunter-gatherer)state, women are pregnant a lot, and thus ovulate less, and thus keep on ovulating to a later age, typically beyond 40. Note that more pregnancies does not necessarily mean more children since child mortality is high.
(*) Most literature uses females as examples, but don't talk about males. I don't know if it is assumed that females take a bigger part in their children's first child delivery, or for other reasons.
And many of those issues can be mitigated by medicine/dentistry. A more hard limit is parts that don't replace at all, like most nerve cells including the brain and some glands. That limit is more 75-100 depending on the individual's genetics.
It was rare to live past 30. Either tribal warfare, or disease, or being killed by an animal while hunting, and so on.
Still is. Knowledge is based on old testimonies from both (mostly Western, sometimes Arab or Chinese authors, and directly from the "native" side), combined with current experiences of hunter gatherers in the Amazon to root out old biases and oversights.
Though I'd guess the average age of natural death usually a bit higher than 30. This because the non natural causes of death depend on region and lifestyle it allows. Not all tribes are in regions where humans majorly compete for resources, nor do they all hunt big game. Actually native tribes are quite good in managing hunting risks, my favourite there is African tribes (iirc Khoisan) using exhaustion hunt that is a lot more work, but probably they still do because it is safer. At the same time it leverages an human trait that is often considered a detail (being fairly hairless and the consequences that that has for sweating).
Fire and the corresponding cooking of food, which decrease the risk of intestinal parasites was probably also an factor that is hard to overestimate (150ka, Eastern Africa).
Disease is always a risk, as 2020 has shown, but also has a strong correlation to the inter-human contact factor, and potentially the levels vary between early civilisations with denser population and contacts while for relatively isolated hunter-gatherers tribes it is lower.
And this is how our ancestors lived for hundreds of centuries. An indirect confirmation of this is teeth which in many people begin to seriously deteriorate after 40 years even if they are well cared for.
If the average age can be raised to 75 and beyond, then I wonder what you define as "serious"
And women can and physiologically should give birth right from the age of 13-14. What kind of long study can there be?
That ability is not fixed and can vary by individual by several years, and it is also not fixed in that it depends on adequate (amount and also quality) food. Primitive tribes possibly always had growth limitations due to dry or cold seasons, and first menses correlates with that. The fact that women stop growing around 15-17 years (even with adequate food) makes that a much more logical age than first menses.
Moreover early pregnancy increases the risk for women (without modern delivery methods) as the pelvic bone structure keeps widening after puberty, decreasing the risk of pregnancy complications. I only saw that as remark, without much info which age would be safe(r), but maybe your ideal age of for childbirth of 25 (or at least the reason why it is not as young as possible) is due to this reason.
Besides, keep in mind that because something in the old times this was a problem causing evolution, this is not really a hard decree that it should be now too. Evolution is governed by bottlenecks, not averages.
We can change this either genetically (live ~300 years) or we can integrate learning directly into the brain via implants.
And I suspect that implants will appear sooner than genetic longevity.
Raising the average age way above 80 will be hard and require technology that is the realm of SF due to the brain cells not replicating. Any claims about it should be considered with extreme scepticism.