Actual leftists don't give a shit about immigration for numerous reasons. In no particular order:
1. Labor, like capital, is a global institution, and there is nothing gained from "supporting labor at home" at the expense of labor "abroad."
2. "Foreign" labor and "domestic" labor is a false dichotomy, because the wages of the one depend directly on the exploitation of the other.
3. If Leftists actually were in a position where they could control immigration, they'd be in a position to dismantle their national bourgeoisie.
4. "National" borders presuppose a system of private property and are illegitimate from the get-go. No one has the right to arrest or remove anyone that wishes to peaceably travel or settle.
5. "Immigration" itself is a bourgeois concept arising out of 19th century nationalist sentiments and is inherently reactionary.
No, borders are not natural and they haven't "always existed" and the historical trend is that no one gives a shit about "borders" except for wealthy aristocrats marking off where their property ends and the property of some other aristocrat begins. If you're not an aristocrat, you're property, and arguing for borders is arguing to be someone's property.
Walls and fences are artificial physical things erected to enforce the private property rights of those behind them and control the flow of people within them and supporting that is supporting giving someone else the power to decide where you can and can't go and when, which is exactly what we see now where you have to have a passport and governmental permission to leave or enter an arbitrary geographical location. Borders are a spook and you're a massively spooked class cuck for wanting them.
No, little brainlet, not enforcing the bourgeois concept of borders isn't the same as "lol do whatever you want." Bourgeois borders under the current capitalist framework don't exist to keep people out, but to keep people in. There's nothing stopping a prole from some bombed out shithole from getting into your country and stealing your job, border or no border, if they've got the money, and someone is always going to be willing to give them the money, whether its capitalists wanting to undercut so-called domestic labor or some desperate refugee willing to take out a bunch of loans from the Triads to get smuggled in.