There are different kinds of immigrants. There are ones who immediately add to the economy, typically professionals, and there are the uneducated undereducated who have low skills no skills whose contribution can take much longer to realize.

Many countries want the highly skilled to immigrate, and conversely countries don't want them to emigrate (brain drain). No one country with low skills emigrants puts of a fuss to keep them, they are happy to let them go and they have no concern about lowering population or concern for potential tax base loss.

In the end the question is, do you want to regulate immigration or just let anyone and everyone in? There is no reason to have two tracks where the ones who want to go the legal way have to wait years while others can just go the alternate route with few consequences.

And, w/re Mexico, they also deport a good number of illegal immigrants into their country, so it's not like they think one way and the US an Europe and Japan and China etc. think another way.