Sure, the UK has only been one of the most open countries in the last century. Have you ever been to London? Heck, my home town of 2,000 people had more diversity than I have ever seen in Buenos Aires with its millions. I agree that its easy to waltz through the borders here compared to the UK, but here's the thing.
Argentina is open to "us, our children and all the men of the world" but most of us, our children and all the men of the world don't want to live in Argentina. They do, however, want to live in the UK or a similar country which may explain stricter (rightly or wrongly) immigration laws.