To me, “undocumented” suggests that you are here legally but you just don’t have your documents. Suppose an American citizen lost their driver’s license or their birth certificate. They are still American citizens, they are just “undocumented” because they don’t have their documents. And there are procedures available for them to replace their lost documents in such a case.
Whereas the illegal aliens are here illegally, so what’s wrong with calling a spade a spade?
Sadly, all too often, the illegal aliens have documents.