The Amish are extremely business savvy, shrewd negotiators, and have no issues being active members in the economy. They also own vast tracts of very valuable land (especially in Lancaster, PA). Combine that with being frugal and austere, and it's a recipe for wealth.
For childcare, their community focus let's them share the burden amongst the larger group. Additionally, children are not nearly as coddled and are expected to contribute to the family's work, and help co-parent their siblings.
Compare this to the average nuclear family: underpaid, barely any savings, most likely rents, and lucky if they have even one family member nearby that can share the childcare burden.
Lancaster, PA resident here. Many, possibly most, Amish are not farmers anymore. To your point, a lot own businesses like lawn care, grocery and hardware stores, tourist traps, and construction companies.
Since childcare is mentioned, I would be remiss if I did not point out that the Amish have a disproportionate rate of child sex abuse. Offenders often get off because the Amish community pressures victims not to testify. Victims are sent to re-education centers. It is pretty gross what goes on in plain (pardon the pun) sight. But they bring in tourist dollars. Most Amish are lovely of course, but their lifestyle has a very dark side.
Amish are pretty much like everyone else though, there are dirt-poor Amish communities out there to counter-balance your land-and-small-business-rich ones.
I will say this, if there is one thing I can do for my child (other than learning proper money management), when the time is right I will help them with the down payment on a home. Holy crap it's so much more important than renting. It seems like a hassle, I know, but building generational equity gives you such a leg up in the world.
In many areas, the amount you pay in rent isn't much different than what you pay in the ITI parts of PITI (principal, interest, taxes, insurance) plus the maintenance costs. On top of that, the difference between mortgage + maintenance and rent could be invested and growing over time.
There's no guarantee that buying a house will leave you richer than if you'd rented during the same time. Check out this calculator to explore your personal situation more closely, and examine the assumptions you make about growing wealth.
I know from personal experience, owning my first home, that I almost certainly would've been better off renting over that time period and investing the down payment and higher monthly payments than I ended up with having that house and equity. Sometimes you get lucky - and house prices go up and you sell at the right time (assuming you switch back to rent OR manage to then buy in a market where prices are lower than average.)
I'm going to go ahead and disagree with you. A house is a form of forced savings, which is why it works so well for people, but you absolutely can build up wealth while renting.
It is for sure possible, no argument, but the actuality of it is relatively small, while the renters are putting in equity into someone else's pocket =/ Your "rent", as it were, goes towards something (even if a large portion of it is interest.. and extra payment a year towards the principal goes a long way).