Trump just referenced the Statue of Liberty... all while his biggest platform is to stop immigrants from coming to the U.S. unless they have value. Did his grandfather have any special skills when he came to the U.S.? He was a barber's apprentice... not a doctor, or lawyer, or teacher... under Trump's own policy his grandfather wouldn't have been allowed to come to the U.S.
At that time what was valued was unskilled raw labor. And while a nice poem, and reflecting a dramatized version of some people's thoughts at the time, it wasn't the official policy of the United States government. All had to go through places like Ellis Island. Plus there was no safety net, and people were expected to suffer a generation or two for the chance that their children or children's children would have a better life than the one they left.
You are comparing our current situation, where we have too many undocumented immigrants, to a time when our industries were starved for labor.