Should immigration enforcement be given to the states?

I know some of you are going to immediately bring up Arizona but please try to hear me out here. The country as a whole seems hopeless on the immigration issue, at least in terms of any type of consensus. Should President Trump maybe change his tactics, and either by a Constitutional Amendment, New Law or Executive Order essentially announce that the federal government would no longer be involved with enforcing immigration and that immigration enforcement will now be up to the states.

This would essentially allow the liberal blue states to have their whole "open border" policy while red states would be able to actually have a strict immigration policy. Now I know the first question would be how this would work, since immigration to a state like Arizona would be compromised because California would let the immigrants flood in. There is a solution to this but many of you won't like it.

It would involve open interstate commerce and transportation between the states coming to an end. In a way it would go back to the way the constitution originally intended the states to be, as almost different countries. Every state, if they wanted to, would be able to build a wall around their state and institute checkpoints at all entrances to their states, including road, marine and air traffic. The days of being able to freely travel between the states would be over.

An example would be air travel, air travel between the states would essentially be similar to traveling out of the country. A state ID would no longer be enough, you would need a passport to travel (either by air or car) to another state. When arriving at that state like arriving in another country you would have to go through customs. If someone is actually coming from outside the U.S. they would have to go through both U.S. and state customs. Yes sadly the days of being able to get off a plane, go down to baggage claim and immediately leave would be over. In terms of car travel it would be similar to if you were to travel to Canada today.

There could be regional agreements, for example all of the south could agree to the same strict immigration policy and therefore have "express lanes" and not have to show a passport to go between those states. California, Oregon, Washington and Nevada could all agree to have open borders and of course would not require a passport. But overall each state would set its own immigration policy, have its own border security and possibly a border wall.