This is a really important issue. I'm sure all the folks from China and India who waited 10 to 15 years to get a Green Card will be really happy if an amnesty happens.
By 'irregular' we mean impoverished desperate people? Who have no means to afford paperwork and lawyers? Being fair to the (relatively) wealthy is a strange sort of fairness.
I'm speaking of fairness in opportunity. Someone in the Gabon should not be at a disadvantage just because they can't simply cross the border. We should set a quota, 1M, 2M, whatever, and distribute that fairly among all wanting to immigrate.
We set the rules. We have not achieved WH Bushes thousand points of light new world order single government. We look out for ourselves just as China, Mexico, Singapore do.
Some of the issue comes down to fairness.