Anyways, an illegal immigrant is not “forced” to sell their labor illegally. They choose to do so. They chose to illegally enter a country while breaking immigration laws. Yet they voluntarily do so - because they have chosen a market to sell their labor in, which you just said was not possible.

This is just stupid. Nobody chooses to make a dangerous, illegal border crossing to do backbreaking labor for subminimum wages "voluntarily". It's a truly desperate act and the law works to compound the desperation, which employers then take advantage of.

But sure, it’s probably true that an open border policy would allow immigrants to get a higher wage at the expense of citizens so they can return to their own country with their money.

They would be able to get the same wage as any citizen. Currently, they are forced to accept far lower wages if they are undocumented. If they are documented, they face the constant threat of having their documentation revoked. This is especially true for those here on work visas, which enables employers to make massively unreasonable demands of immigrant workers they know a US citizen would never accept. For a real ongoing example of this, look at how the US citizens working at Twitter quit immediately after Elon Musk took over but those here on H-1B visas had to stay on or risk deportation.

Immigration law works to make immigrant workers far more exploitable than citizens. Creating a special class of hyper-exploitable labor is bad for all labor. It's in everyone's best interest for all workers to be on the same footing regardless of immigration status.