Problem with Mexico is it is trying to use "western" tactics in a Latin American problem.
They hardly did do that under Felipe Calderon, under whose administration the army dug mass graves wide and deep. To what end? Your view is way too narrow. The current government does what it does by popular demand, on the grounds that all previous attempts to curb the Cartels failed miserably.
Mate, the drug problem of the Philippines doesn't even move the needle in comparison to Mexico's. That country's issues run much deeper, they run deeper even than Colombia's during Escobar's days. No one wants to admit it, but Mexico's drug cartels are as powerful as they are because they're outgrowths of the nation's very culture.
Some of the most successful Mexican musicians sing the Cartels' praise, murals and television shows portray them as heroes, and the country's youth watches and listens. Young men flock together in droves to join their ranks – not to escape poverty, mind you, but to live what they think will be a manly life, a life of adventure. You'd have to do something about
that before other measures (violent or otherwise) could even begin to make a difference.
Besides, Mexico's security apparatus is so corrupt that according to Borderlandbeat (a knowledgable blog on the Mexican Drug War), it's not unlikely the majority of the Cartel members did wear or do wear the insignia of one of Mexico's uniformed services.
The situation is so bad that it is, quite frankly, amazing Mexico still enjoys the resemblance of a civil society. However, the sad truth is Trump's suggestion is probably better than anything the Mexicans could come up with, although it is utterly unfeasible as well. You'd have to bring in tens of thousands, perhaps hundreds of thousands of soldiers, police officers and civil servants to completely uproot organised crime in Mexico.