my great grandfather did
when entering America by way of Ellis Island having a sponsor and a job as a farm hand waiting
for him.

After 1924 Ellis Island was primarily a detention center for those denied entry or those being deported.

The primary problem with deportation is not having the money for the processing out with due process and the actual deportation. If we cut out due process it gets cheaper, but then we aren't a nation of laws and the due process is in the Constitution. We also want to be humane. It would be difficult to cut out the deportation - Mexico would be right to be upset if we dumped everyone there.

It's still true that most of our illegals are overstays. We could streamline and lower the cost of due processing them out, but it still takes money and a willing Congress. The Republicans haven't dealt with that because it's a great issue for elections. Fear is a great motivator, especially for those not inclined to think for themselves.

Trump passed up the money, now he needs it, so he pushes self deportation and takes money from the military budget.