right off the earth....
Sure those mexicans are ruthless and cruel, but they are insects compared to highly trained, cool as ice, soliders
Can you imagine if everyone who is addicted to drugs provided by the cartels had to quit cold turkey? We don't want to have to deal with that.
Better to remain silent and be thought a fool than to speak out and remove all doubt.
2 words: "Decentralized structure"
In theory a couple of well trained soldiers could just erase the top level of any crime outfit. Hell, you could put a very effective end to gang violence inside the US with a brigade if you really wanted to.
The problem with something like the cartels is a) finding the people at the top (multiple homes owned through proxys, changing locations...it's like finding Bin Laden all over again) and b) preventing instant replacement (You kill one drug lord and 3 others have taken his place before the bullet hits).
Especially "b" is a huge problem. Because the production (fields and chem labs) are spread out you can not effectively destroy them so the new boss would still have access to the complete infra structure and could seamlessly continue operations. In the end it becomes a loosing battle. You need 6 months to find the boss and his second in command will take over and have the whole thing running one week later. And then you spend the next 6 months looking for him.
And then of course there is the legal problem of using military resources for Law enforcement purposes and of the sovereignty of other countries...