It's not so simple to get rid of "asylum seekers".
If you go back to the late 90's the border patrol started encountering something new. In the past illegals would swarm in and simply try to hide, etc. But, all of a sudden 20-25 years ago, the border patrol started noticing that when they came across these people, most of them would claim asylum. It was then, our government concluded that the word apparently had got out south of our border, that if a person claimed they were escaping government oppression, tyranny, hostility etc, they would be treated more like we have treated Cuban refugees once the Communist took over. It's been a huge problem and unless we change our laws and policies, this country is finished. We will be nothing more than what we see south of our borders, where crime and poverty are the norm.