Root cause it. The USA does not have an illegal immigration problem. It has a "huge, slow immigration bureaucracy" problem that makes the legal path so slow and difficult that people are incentivized to gamble on illegal paths.

People who abuse birthright citizenships are, by definitions, not illegal immigrants. But even if you count all of them as 'unwanted' immigrants - how many % of total immigration to the US is result of those birthright laws?

A right enshrined in the Constitution is not a "loophole".

Most countries with a standard of living that even barely better than their neighbors have an immigration problem. There is a whole continent call Europe that is fighting off migrates and last I checked, birthright citizenship is not a thing there.