Leaving aside the dubious benefits of police, Amish pay the same taxes as everyone else- with the exception of Social Security and workers' compensation, which they pay through their church. Those taxes entitle the Amish to their share of the national defense buff.

https://marketrealist.com/p/do-amish-pay-taxes/

> This means they aren’t truly independent. They’re dependent in a way they could never afford to pay for themselves.

That would seem to describe most, if not all, citizens of contemporary societies. Could you name someone who you consider truly independent? As the saying goes, "No man is an island."

The relevant comparison here is to other citizens, not to other states.

Yes, this hypothetical country would be peaceful and immune to the (justified) criticism the US receives over its intervention in foreign wars. However, think of all it (and the world) would lose. The rest of NATO would have to invest way more in defence in order to hold off Russia and China. The rest of the world would have to invest a huge amount in R&D for things like medicine and technology. And the only thing keeping this hypothetical "Amish United States" from being invaded are the oceans.

It's hard to take these sorts of counterfactuals too far though. On the one hand I might say "then the drug cartels in Mexico could invade the Amish United States and enslave everyone" but then it would also be equally valid to say the cartels would never exist in the first place if it weren't for drug prohibition and the demand for illegal drugs in the US. Still, I don't see how one big Amish nation would defend itself from gangs moving in and stealing everything they've got and enslaving people.

No, it isn't, and that's not how game theory works. No one is suggesting that everyone be Amish, and it seems fairly obvious that the Amish would act differently (e.g., invest in self defense) if that were the case.