That doesn't describe current US policy, which prevents people from coming that would make the country a nicer place to live, and lets many people in that wouldn't. By design, it even brings in random people.
I'm not describing a policy, I'm describing an ideal. (A simple concrete policy proposal is below.)
You said:
> Here's a simpler proposal: anyone from anywhere can come here and take any job.
So that doesn't describe your policy proposal either. Plenty of people can hold down a job and make the country a worse place for others, or a subset of others, simply by competing for resources, driving down wages in the sector they work in, by being a criminal, or by voting immorally.
I want to let everybody you'd let in, except for people whose immigration would make the country a worse place. Define that ideal as you will.
As a pretty good approximation, we could limit immigrants to those that could qualify for military service.
> myself included, I'll be honest—feeling uncomfortable with that is part of why I left
That's also a reason why I left. My policy as a national policy, is to make the country a nice place for all of its citizens (except criminals and slovenly degenerates) to live in. So that includes people that might like to move from Arizona to California. They're making their own lives better, which counts for something.
> I think that this country would be a nicer place to live for myself if I can hire whomever I want for my team regardless of citizenship and without big government second-guessing my decision
If you're like most employers, that means you're happier if you get to drive down working class wages, while you get to reap greater profits from your pre-established position in the market. That's good for you, but not good for the average American.
To make my goals a little more nuanced: Economically, I want only the smartest immigrants, which do advanced stuff like start companies, work for them, or work in healthcare, which drive up the demand for working-class labor, letting average Americans negotiate a better piece of the pie, while driving down the cost of their healthcare. Culturally, I want supply limited so that immigrants assimilate, and I want all the immigrants and their children to be crime-free pro-life Republican voters. :-)