Keep in mind, Australia also has a very low population density, but you'd have trouble populating the interior.
New Zealand has a very low population density, and is essentially a large national park. Certainly they could up that population density of 16.4/km^2. Should New Zealand aim to increase its population five to ten fold over the next 50 years to catch up? Is New Zealand an "anti-immigrant" country for not allowing this kind of growth through immigration?
You can say "yes", but then you'd have a tough time identifying a country that isn't "anti-immigrant", and I think the US would come off as one of the more immigrant-friendly nations out there. Not the most so, but pretty high up on the list.
Yes. I do think the US is one of the more immigrant-friendly nations, but the numbers admitted can't be divorced from their context.
No immigrant is going to move into the middle of nowhere; they are going to move to cities or towns. People vs. total area is a misleading number.
In any case, this is a curious objection to raise in a thread about a story documenting the inability of rural farmers to hire a productive labor force following a change in the law. Quite a lot of immigrants work in the agricultural sector and live a good way away from major cities.