I'm really amazed sometimes when I debate with some of my hispanic friends about immigration. They refuse to believe that immigration laws exist for logical reason
Immigration laws are like any other big set of laws (taxes, labor regulations, etc.). There's a bunch of them, and they're a result of different groups at different times pushing for different goals with different results. There are reasons they are the way they are, but it's not inherently logical or good.
It's generally a bad idea to leave a law on the books when it isn't being enforced. An unenforced law is usually an unrealistic one, and it's one that can be selectively used as a bludgeon against certain groups. Either do what it takes to put it into action, erase it from the books, or write something better.
But yeah, you're right that the people who care the most about this, on both sides, are going to approach this from an emotional perspective rather than a cold, logical, economic argument or something. Which is why I don't think anyone will be able to come up with a solution that both groups are happy with.