"My expectation would be if we were to allow open borders, then it's understood that these workers are not illegal...and employers can't take advantage of them any longer."
That's exactly right, and there's a reason that's non-obvious to most. Migrant workers have a vast network of underground support in one another. They share information about how to make it in the US. They help one another find jobs, housing, childcare. They teach one another how to gain access to whatever services are available to them. These people are capital O Organized, and if we give them legal status the first thing they're going to do is unionize across every industry in which they've gained a foothold. It could spark a renewal in support for unions across the country. Everybody that has a stake in the current status quo is scared to death of that.