I'm one of 4 and DP one of 5. We have 2 and all our siblings have a maximum of 2 or none at all.
I think large families these days are a lifestyle choice. More so than having 1 or two.
I'm in the thick of it currently with 2 under 2. I've met a couple of mums on maternity leave on their fourth or fifth. Ive met one of her seventh!
They've all varied in terms of class/income. But one thing they all have in common is that it's a way of life. I'm NOT saying this in a bad way btw. But it has to be. Currently my life is hectic with 2 under 2 and really full on. But I know it's just a phase. In 2/3 years it will be completely different. I'll resume my hobbies and social life. I may go from 3 days a week to more days. My dining room will have an actual dining table in it and no longer be a playroom. I will no longer have a huge nappy bag/prams etc whenever I leave the house.
But with big families it isn't a short life phase. This hectic/busy phase is it. It's a way of life and you've gotta be 100% in.
These mum's I've met including my own mum and in-laws (not met the dad's) live this busy in 'the thick of it' way long term. The mum's I've met have been wonderful, kind, knowledgeable women who really adore family life. They'll have the full sha'bang, all in. They'll have the family pets (dog, cats, hamsters, guinea pigs etc). They'll have house set up long term for kids e.g swings in the garden installed into the concrete so can't be folded away. Everything is set up long term for that lifestyle.
Their social life is usually other mum friends or family. Their hobbies are volunteering at their kids hobbies etc.
To be honest I don't think you can have a big family and not be this way, especially if you want to be a fully present parent. These mum's love it and it's their lifestyle choice.
So long as the kids are cared for and loved it's no issue really.