While I agree to your point, there's one sentence that hits a pet peeve of mine:
> For most of our history, most humans societies were only barely able to feed themselves. All growth in food supply was quickly matched by population growth.
This, like most clichés isn't strictly wrong, but it's not very true either, at least for agrarian societies. Almost since the beginning of agriculture, agrarian societies have experienced food surpluses, and that's what made the cities appear (as in a pre-industrial society the urban population feeds from the surplus of the countryside). And, at least in Western Europe, until the late middle ages there was a lot woodland completely fit for agriculture[1] that weren't exploited yet, leaving a huge margin for population to grow (and it did in fact, grow). So in most of the history of agriculture, again at least in Western Europe, population wasn't simply linked to the size of the potential food supply. It was probably much truer during the early modern period, when most woodland had been converted (even though the quick adaptation of the British agriculture during the continental blockade showed that there was again quite some margin there).
[1]: we know that they were fit for agriculture, because by the end of the middle ages, they were cultivated.
> Almost since the beginning of agriculture, agrarian societies have experienced food surpluses, and that's what made the cities appear (as in a pre-industrial society the urban population feeds from the surplus of the countryside).
You are confusing an individual-level surplus with society wide one. It is true that a single farmer, with abundance of land, can produce great surplus of food, much more than he or his family is able to consume. However, on a society scale, there was very little surplus overall. In better years, food was quite sufficient for everyone, sure, but in worse years, people starved, especially children, elderly, and the destitute.
This is immediately obvious by looking at the population figures. The population growth everywhere was glacially slow by early modern standards, except when a group moved into previously unoccupied territory, or into territory occupied by groups with with worse food production technology.
Consider, for example, population growth in colonial America and in early decades of USA to population growth in UK. If UK population grew as fast as New England in years 1600-1800, by 1800 UK would have had something like 500 000 000 people (half a billion) living in it. Such rapid population growth was only possible in New England thanks to abundant land, very little of it has been previously used for cultivation by native Americans.
Or look, for example, at the rapid population growth in Africa today. Why hasn’t Africa ballooned to a billion people already in 1800, despite millions of years of head start? Simple: they simply couldn’t sustain populations so high with technologies available to them.
Given right circumstances, the population growth and fall are extremely fast on a historical scale, though it is hard to intuitively comprehend for humans due to us living on a single human lifetime scale.
Technological advances during the middle ages made more land fit for agriculture.
>> During the medieval ‘agricultural revolution’, new forms of cereal farming fuelled the exceptionally rapid growth of towns, markets and populations across much of Europe. The use of the mouldboard plough and systematic crop rotation were key developments and led to open-field farming, one of the transformative changes of the Middle Ages.
> For most of our history, most humans societies were only barely able to feed themselves. All growth in food supply was quickly matched by population growth.
This, like most clichés isn't strictly wrong, but it's not very true either, at least for agrarian societies. Almost since the beginning of agriculture, agrarian societies have experienced food surpluses, and that's what made the cities appear (as in a pre-industrial society the urban population feeds from the surplus of the countryside). And, at least in Western Europe, until the late middle ages there was a lot woodland completely fit for agriculture[1] that weren't exploited yet, leaving a huge margin for population to grow (and it did in fact, grow). So in most of the history of agriculture, again at least in Western Europe, population wasn't simply linked to the size of the potential food supply. It was probably much truer during the early modern period, when most woodland had been converted (even though the quick adaptation of the British agriculture during the continental blockade showed that there was again quite some margin there).
[1]: we know that they were fit for agriculture, because by the end of the middle ages, they were cultivated.