You came here...you either became a citizen or didn't. Either way you were counted.
There was no welfare state then.
There was an untamed frontier with land aplenty.
There was no ISIS or muslime terrorist cabal.
Laws were enforced and violators punished. Immediately.
This was a largely agricultural economy; industrialization had not yet taken hold.
Immigrants did not dare to demand a cornucopia of benefits; they were expected to be self-sustaining.
You're comparing apples and oranges.
They didn’t have massive welfare systems that we have today. Now we have American taxpayers paying for the healthcare and education of immigrats. That was never the case before. They had to come here, assimilate, and sustain themselves.
Today, these immigrants come from 3rd world countries and leech off our system while voting for more big government.