The only thing why that needle doesnt move is because Asian governments are draconian when it comes to people that try to over power it. Specially criminals, this is where a "western" mind set about human rights can go wrong when you are not in that developed state yet.
Americans would fail miserably at fighting the cartels, for the simple fact that drugs is a cancer and curing it it will not be a pretty sight.
You didn't get my point, and it seems as though you disregard the 2006-2012 period of the Drug War under Felipe Calderón. Mexico's government most definitely didn't have a "mind set about human rights" in that period. Scores were killed or disappeared under the auspices of the Mexican state.
It was of no avail, and no, the Americans wouldn't fail miserably – both for the very same reason.
You suggest to respond with draconian force, but you ignore that somebody needs to carry out that response – and that'd be a heavily unreliable, insanely corrupt security apparatus. You forget that in order to cut off the Cartels' supply of manpower, you'd have to re-engineer Mexico's society from the bottom up – and again, you don't have the muscle to do it.
The Cartels have been killing hundreds of teachers, journalists and clergymen who'd denounced their deeds. These are the people whose help you'd have to enlist, but how do you want to protect them, especially if their potential killers are just as likely as not to wear a uniform?
Mexico ticks almost all the boxes of a failed state. The only strategy to alleviate its crisis that wouldn't span over generations is to remove every police officer, every soldier and every public servant whose loyality isn't beyond any doubt, and replace them with people raised and educated as far away from the Cartels' power bases as possible.
The government did try to implement that strategy three times, and saw successes each time.
First they sent the federal police to replace the unreliable state and local police forces. That worked until the Cartels had learned the federal police was just as corruptible.
Then they sent in the army, which did its job for a while until history repeated itself.
Last but not least, they replaced the army with the navy, whose members can be more easily shielded from Cartel influence due to the nature of their service.
But from what we can gather, even the navy's resilience to corruption has been developing cracks. The reasons seem obvious enough. They're not paid enough, and their families aren't safe.
That's why bringing in a foreign force could actually make a difference. And as far as I know, such a scheme was actually considered under Bush and Obama. It was certainly considered to bring Mexican recruits to the US, train them there and allow their families to stay for reasons of safety as long as their loved ones operate south of the border. That alone might actually make a difference.