Great take on the immigration problem, i myself would view this in the lens of a population geographer, where population change is dictated by the push and pull factors of a region/country, and in line with your analysis, the push factor from their home countries and the pull factor from europe is just too big, hence the massive immigration wave that overwhelms border officers and border patrols. The solution? Improve their home countries so that they are more inclined to stay compared to leaving for europe.

All in all, a great post and i agree with most of your analysis, keep up the good work!