Many in the US (and to a lesser extent Western Europe and Australia) seem to answer that last question with a "yes." It's never addressed why border controls by China, Mexico, or really any non-Western country aren't also "reprehensible."
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.