The media-friendly hyper-Christian families are, I think, very unrepresentative. Most of these families don't have a lot of money. A lot of the churches who promote this lifestyle discourage higher education. The Duggars' group basically doesn't allow it. Some slightly more liberal ones do, but only at religious universities like Bob Jones or Liberty. They also tend to live in less expensive parts of the country, which makes housing more affordable. Some of them also don't believe in health insurance, like the Duggars, so they're just not paying for that either. They do those Christian "health shares" that aren't real insurance.
The LDS church (mormons) doesn't routinely provide members with assistance. Quite the opposite: you tithe 10% of your income and they check. If you don't pay your tithe, you don't get your temple recommend. What the church does give you are connections. If you're willing to work, you will have a job. The church also heavily subsidises tuition at BYU, which helps encourage LDS youth to marry young. It's not uncommon for them to marry while still at university.
The US taxes on joint income, which is more favourable to families where one spouse earns significantly more than the other. There is a large tax free allowance (If you don't itemise) and child tax credits. The tax system is hugely complicated but families with children do fairly well; the problem is that you're left to pay more of your health and child care costs. Salaries in the USA are higher in many fields. Housing here is as bad as UK, Canada, Australia if you're in a major city, and yes groceries are higher... though IME still not as bad as Canada or Australia.
Not all American houses are huge. They always show massive ones on TV and often news articles cite average sizes of new build houses--not all houses. New build size has gone up substantially over the years, not just because of buyer demand, but because of builder profit. The municipality will say to the builder, you can build X houses on Y acres. They can't build more houses to increase profit, but they can make each unit bigger as long as they don't exceed the buildable area per lot, and it's all profit since making a house bigger is relatively inexpensive. Since a lot of municipalities insist on relatively large lots, they can build massive houses. My house was built in the 1970s. It's nicely sized (about 2k SF), not as big as a modern one would be. But I have the same if not larger land size as a new build. Nowadays they'd put something nearly twice the size on it if they were allowed, though my county now insists on higher building density in most areas.
American housing stock and size varies quite a lot by age and location. So in East Coast cities you have row houses (terraces) that are quite like what you'd see in Britain. In LA and San Diego there's lots of small bungalows. 1950s suburban houses are relatively small: the original mass produced Levitt house was 750 SF (most have been renovated and expanded now) and the ranches and split levels were 1200-1500. There's still loads of Americans living in houses like that.