Immigration and customs are federal issues, not state issues, no matter how you slice it.
The problem isn't that there exists an organization to enforce, but the entirety of its approach ("find people to kick out / take to concentration camps"). Within the framework we have today, something like a non-citizen being convicted of a crime (handled by local/state) being handed off to ice to deport to the appropriate country of their residence? Sure.
But also borders are pretty stupid if a lot of the other stupid stuff around it goes away too.
Nothing.
Before DHS is was handled by the treasury, labor, and justice Dept's (moved around in various ways over the past ~130ish years), the most significant change being immigration under the DOJ in 1940 (for... Somewhat obvious security reasons for the time).
DHS just absorbed all the different groups under one shitty lead. The excuse at the time being terrorism.
There is zero reason customs shouldn't be under the treasury, immigration under labor, and enforcement (as in managing the deportation of those convicted of violent acts, or pursuing smugglers identified by customs, so on) under justice.
The reformation under DHS was specifically designed to militarize.