An abundance of food means an abundance of offspring until there is no abundance of food. You have to make people serfs for them to spend their time with anything but increasing their family size and thereby increasing their power and influence. So maybe they weren't slaves, but for sure they were serfs.
This book explains it extremely well and backs it up with data in excruciating detail (which you can read or skip if you're convinced early on).
People think that Malthus predicted exponential population growth, but his actual observation was exactly what the above comment described. Growth in productivity would lead to growth in population until wealth per capita reached the same point it was at before. No improvement in productivity would ever actually improve the human condition, just increase its size. Malthus was absolutely right at the time he made this observation of his so called "Malthusian trap".
The observation you make about the modern world and lower birth rates started very abruptly not long after Malthus published his findings. The industrial revolution literally invalidated what had been true for all of human civilization up to that point.
That's also with modern medicine. Back in the day you had to have lots of kids because nearly all of them died and you needed someone to work the farm and care for you in old age. In modern society, they're viewed more as an expense.
In the modern world, the population is put through 9 or more years of indoctrination during formative years to conform to a different system. Before then it was have as many children as you can, because when they become adults they can have no stronger allies than their brothers.
