>>They don't qualify to come to the USA

FWIW, an Australian politician claimed a while back that 90% of asylum seekers arriving in Australia, destroyed their passports or papers en route to make it more difficult for Australia to deport them again- where to, and with what travel documentation? In response to this and because of unseaworthy people smuggling boats that increasingly needed rescue, Australia moved its asylum seeker camps to remote island locales in New Guinea, Nauru or Christmas Island and declared that anybody who destroys their papers automatically goes to the back of the queue.

Australia has been widely criticized for this policy, but these days there are far fewer people smuggler boats and no perverse incentive that destroying documents before rescue or delivery to Australian soil makes it difficult to get you out again. In international law it appears legal, since the asylum seekers are not sent back to their war-torn or oppressive origins and are provided food, shelter and medical care in the camps. There are reports of sexual abuse and other unsafe conditions that Australia insists it does its best to control. Australia also says that refugees are not detained and that in fact if the refugees wish to leave, Australia will cover travel costs for any camp resident, to any country that will take them.

NZ has it easier because it has a Trumpworthy moat that is quite dangerous and inadvisable to attempt without stopping in Australia first. I can't remember any people smuggler boats making it to NZ. Also airlines flying into NZ have to ensure visas etc are in order at the port of origin, which removes any benefit from destroying your documents or claiming to be an unaccompanied minor that causes big issues elsewhere.

AFAICS, the US takes more Syrian refugees via UN programs than anybody else, which is why Trump's order would have stung. Meanwhile Turkey has the largest number of refugees in its camps, but that is intended to be temporary. Saudi Arabia refuses to take any, though it will fund mosques for Muslim refugees accepted by Western nations.