Well yes, noncitizens and immigrant citizens alike cannot become president. However, I agree that noncitizen is not a specific enough term. A noncitizen is everyone who isn't a citizen of a country, whether they live there or not. It implies neither legal nor undocumented status.
It is SUPER interesting that we are now in a comment period for an LCSH change that has hit the national news cycle. I can't remember that happening before.
Did any of LC's previous announcement say 'undocumented immigrants'? Here's the relevant text from March 22:
[we'll change it to] "Noncitizens and Unauthorized immigration, which may be
assigned together to describe resources about people who illegally reside in a country."
That seems ungainly. Again, why not just use the widely used colloquial undocumented immigrants?