Here's a simpler proposal: anyone from anywhere can come here and take any job. If you leave your job, voluntarily or not, you have 90 days (up from the current grace period of 60 and strict rule of 0) to find another job. If you've been here for a few years you can apply for citizenship, independent of your employer.
The primary objection to this is crowding out the labor market, to which I'd say: protectionism doesn't work. If there are people in another country willing to do the same job for cheaper, the invisible hand will figure out how to move the jobs there, perhaps through competition. Fighting the free market isn't going to work: figure out how to work within it. (For instance, offer a UBI for citizens only.)
The primary objection to this is crowding out the labor market, to which I'd say: protectionism doesn't work. If there are people in another country willing to do the same job for cheaper, the invisible hand will figure out how to move the jobs there, perhaps through competition. Fighting the free market isn't going to work: figure out how to work within it. (For instance, offer a UBI for citizens only.)