Unless the Mexican government gives them a travel visa in the US airport, they cannot even board the plane. This is why the “kick them across the border problem.”
The problem is, We have ALREADY DONE THIS before, Eisenhower didn’t give a rats ass what Mexico said or Did, he JUST DID IT and Threatened Mexico with WAR if they balked.
See Operation Wetback
The difference between then and now is that then, northern Mexico was very underpopulated, and once you were kicked out of the US, you had to go south, or starve.
The situation today is more like the Mexican revolutionary period (1910-1920).
The threat the cartels pose to southern US cities is close to that posed by Pancho Villa when he carried out his attack against Columbus, New Mexico. Villa was fighting the Mexican government, so this really wasn’t their fault. And when the US tried to respond, with the fruitless Pancho Villa Expedition, the Mexican government still had to put its foot down and ask the US to leave.
The US was willing to fight a brigand like Villa, but had no impulse to go to war with Mexico over it.
And thus it would be to carry out a fight with the cartels in Mexico. Except they have much better weaponry, signals and communications intelligence as good or better than the US Army units sent after them, and a LOT of money.
Bottom line: every Mexican criminal we would throw across the border would become a new cartel fighter, whether they wanted to or not. And the cartels would likely start to get foreign military advisors.