The Amish absolutely are actually a great example of the type of immigration no nation should want.
but... what does happen as soon as someone in their community is seriously ill or whatever they are at the local hospital, and its usually indigent care because they don't believe in medical insurance.. When they have structure fire, they call the local brigade to help them put it out but none of them join or become members.
I think you need to be pretty careful about painting with this broad of a brush. In cluding a lot of your other comments about not participating in the economy. Amish communities vary GREATLY by their leadership. Some of the Amish I deal with run a buinding supply store. They have computers, cell phones, CNC stamping machines, propane and diesel fork lifts, etc. All the kids working there have fire pages hanging off their belts from the local volunteer fire department. Some of them even drive.
All of that end when the get home, except the fire pages. Those are the only things that come in, after being charged at work. Cell phones stay in a box at the edge of the property by the mailbox.
So as you can see, some of these communities have found way to integrate that still carries on the traditions and customs of their home life. Also, they are far from broke and socialize paying for outside medical care when necessary.
Build a system that even a fool can use and only a fool will want to use it.