Borders are not meant to "control access to wealth and opportunity". One thing they actually do is keep social welfare programs in check. That's just not possible when you can't control the number of recipients of these benefits, much less the number of non-contributors, but it is possible when legal immigrants receiving these benefits can be counted as such.

Where is it defined that ‘borders are meant to control access to wealth and opportunity’?

I meant that seems like something you could argue, but it also seems very reductive and certainly not a given.