Because there are some really big problems in practice. The biggest is wealth inequality at a global scale, there are several billion people in poor countries who would happily move to western nations, likely causing negatives for the poor and rich countries.
The other is that the more me learn about each other the bigger the cultural divide is/seems. The religious right is often derided in the west, but imagine if it was the whole world voting on things like gay marriage and women's rights, animal rights, etc.
Do we expect poor people who take the initiative to move (i.e., not refugees) to remain poor? My impression is that poverty is mostly about opportunity and access to resources, not about personal desire to be poor.
I don't see how social issues would be particularly different from the status quo in the US. If you asked individual states to vote on gay marriage (which was the case until 2015), they'd vote differently. Different states still have wildly different rules on abortion, including places where abortion is effectively inaccessible. And that's not a disaster for the Union. It's even possible for people to move between states en masse and tilt voting one way or another, but that seems never to happen in practice. Even organized efforts with this explicit goal, like the Free State Project, seem to not be succeeding.
Yes, especially the ones with the most means, this risks creating a serious brain from the poorer countries. It also risks wealthy countries becoming too reliant on poor countries paying for education. We already see this to some extent today.
Also, as a species we're very migratory. Huge population movements only really ended when modern day nation states began. Even militaristic empires like Rome couldn't stop them.
> I don't see how social issues would be particularly different from the status quo in the US. If you asked individual states to vote on gay marriage (which was the case until 2015), they'd vote differently
Just how different are they? Some states may be against gay marriage, but is it 51% against or 60%? I doubt there would be states where it's much more than that, but if we took the world as a whole it would be.
No studies I know of though, if anyone has any I'd be interested too.
"This Voyager spacecraft was constructed by the United States of America. We are a community of 240 million human beings among the more than 4 billion who inhabit the planet Earth. We human beings are still divided into nation states, but these states are rapidly becoming a single global civilization."
It wasn't very long ago that the idea that it was desirable for borders to one day disappear was common enough that the President could say so on behalf of Earth. I suppose this was also the era where things like the Schengen visa came into existence. I haven't heard many people on any side of the political spectrum express such an idea recently, unfortunately, and I think that's a goal that the left has conceded without entirely realizing it was conceding anything.