That’s open borders and it isn’t a popular policy with the country, which is why it hasn’t happened. (I don’t think any first world country has such a policy, the USA is hardly alone here)

People are worried that a dramatic rise in immigrants willing to work for less (since it’s still better off than their home countries) would undercut their jobs by affecting the supply/demand relationship of the labor market.

I’m not sure unrestricted immigration could work but I think we could increase the numbers of visas we do give out by some number less than unlimited.