Don't be so sure about that. The U.S. Government has already de facto ceded the national parks along the border and southern Arizona to them, and it shows no sign of reversing this. What's to keep it from ceding the rest of Arizona? Yellowstone? Yosemite? Texas? Montana? California? New York?
"If Mexico cannot police their side of the border, the US will."
Don't be sure about that either.
If the U.S. Government remains in the control of Leftists, I do not expect any meaningful action.
"As for making Mexico the 51st State, there are good reasons on both sides of that argument."
What's the argument in favor of it?
"If the US Military were to go in and take out the cartels and allow the Mexican authorities to reclaim the territory along the border..."
The only way that could possibly happen would be for millions of Americans to come to their senses and face truth and reality. To do this, they must overcome the enormous pressure of Leftist/Democrat politicians; Leftist/Decadent celebrities, university professors, and their fellow Mind-numbed Leftists; and a Free Press that is the Propaganda Machine for all of these.
In other words: Millions of Americans will have to find the courage, will, strength, and intelligence to overcome the Decadence that has Western Civilization in a death-grip and if not reversed--and fast!--will destroy Western Civilization and America along with it!
God help us!
We need all the courage, will, strength, intelligence, and prayer that we can muster!
We are in serious danger!
We and our children!
Will Americans wake up in time to save themselves and their children? That remains to be seen.