Only illegal migrants aren't covered, legal ones are. If you make it available to everyone regardless of their legality to be on the soil you open up a whole bunch of other issues
Like I could just book a one way flight to LA and become a US citizen because reasons ?
https://www.uscis.gov/about-us/our-history/overview-of-ins-h...
That said, overstaying tourist visas (aka just hopping on a plane and then not going back) is a very popular form of illegal immigration into the US.
I'm all for helping people but you cannot import the world's misery and expect it to be smooth, first because it doesn't solve anything, second because it just doesn't work from a simple demographic point of view.