When my husband was researching his family tree, he found that one great grandmother had given birth to 18 children, only 6 survived, not unknown in the 19th century. However, he also found she died of cancer of the womb. I can't help feeling that any woman having that many children would have associated gynaelogical problems as a consequence.
I haven't watched the programme so can't really comment on the individual family, although I imagine that number of children born to one set of parents would be pretty unique in the developed world. The logistics of day to day life for most people would be a complete nightmare. I do remember going to school with a girl who was one of 14, and even the nuns at my convent, given their view on contraception, would make subliminal negative remarks about the size of the family. The three eldest were girls and they descended with a year between them, so I knew all of them. It was an ongoing joke between the sisters and the rest of us that they shared the regulation school hat. We were all scrutinized by the teaching staff regularly to see that the full school uniform was being worn and the sisters were regularly pulled over as only one of them would be wearing the school hat at any given time, their stock reply would be "it's so and so's turn today" I was invited to their house once or twice, not that large, upstairs was just a mass of beds and it struck me forcibly how very difficult life must be with that many people crammed into a relatively small space. I was particularly friendly with the eldest sister and as we progressed through our teens she told me that she hated the responsibility of looking after so many younger siblings and also hated the fact that they were all on top of each other and doing anything like homework was very difficult. It had shaped her opinion to such an extent that she said she never wanted to have her own children as a consequence. Of course she may well have changed her mind as she got older. I eventually lost touch with her but do wonder if that was something she stuck to.
I think large families can work perfectly well, if the parents have the wherewithal to manage say 5 or 6, but 21 is really off the wall in this day and age. Their carbon footprint would be mind boggling, I don't think David Attenborough would approve!