Just do what Ron Paul says. End the war on drugs to eliminate the need of cartels bringing drugs over the border, and cut down on entitlements, which will reduce the number of people who try to come for government assistance. The people who want to work hard and make their own way will still then want to come, and I say they should be welcomed in this case, once they’re shown to not be criminals and not have infectious diseases.
We used to (when you think Ellis Island) let a lot of people in, but there was little welfare/entitlement. People came ONLY to work; if they got injured and couldn’t work, they were sort of screwed, and they lived in largely segregated “ghettos.” We also split up families all the time; if a father was found to have a disease, they’d send him back, if he complained that he shouldn’t be separated from his kids, then they could all go back home together and not be split up. My point is that it’s not worse now than it was, just different.
It is largely believed that you can have one or two things. Open borders or significant welfare programs. It isn’t financially sustainable to have very open borders AND a ton of welfare spending. The US used to be very open and had little welfare. Many of these European states that people tout as being “Democratic Socialist” countries have a lot of welfare, but strict immigration; good luck moving there as a citizen without proving you have the skills and talent, and/or money, to be very unlikely to be a drain on the system.