When a stranger sojourns with you in your land, you shall not do him wrong.
34You shall treat the stranger who sojourns with you as the native among you, and you shall love him as yourself, for you were strangers in the land of Egypt: I am the Lord your God. Leviticus 19:33-34
Yeah, it does have an allowance for immigration. That is great. And it continues in the new testament as well. But at the same time, you said nehemiah built a wall to keep foreigners out. So it depends on what type of person was coming in. I suspect it was just individuals who stumbled into the area of Israel. I don't think it was talking about caravans. In Joshua 9, instead of eradicating the gibeonites, they got deceived and the gibionites put on old clothes and had moldy bread and made it look like they were from a far country, and Israel made a peace treaty with them. But it was against God's will, they became a stumbling block to Israel later. God wanted all the nations that inhabited the promised land out, no slaves no survivors. So I don't think that text talked about a several thousand member caravan. But I could be wrong. I will have to read it again.
So back to the topic:
my only reservation on not doing a wall, would be that humans were trafficked over the spots that didn't have a fence,
but I can't find any solid studies saying that a wall would actually stop or severely hinder human trafficking.
and we know a wall won't stop drugs (see the O.P.)
so really the wall is just about immigration.
and as christians, is it really moral to say to other ethnicities, "hey I won't share my country with you?"
we teach are children to share, but we won't share.
about violent criminals coming over the border,
if we simply did trade school training or vocational training to illegals, they would not resort to crime.
a study done in prison systems found out that if they educated criminals in prison they would not be repeat offenders.
so many private prisons are doing that.
we need to do that with illegals. Give them some way to contribute to society.
Now at this point someone may say (we don't have enough jobs).
but if we did what God wanted, God would expand our borders, and create the needed Jobs.