If stories in the American Anarchy Zone follow stories of travel like Huckleberry Finn, ones in Mexico are tales of chivalry and the knight errant.
Currently, Mexico has seen a return to the semi-feudal Hacienda system that predates the 1910 revolution. Some of these areas are simply run by rich individuals that garnered loyalty, others by police or army units that pacified an area. More than a few are run by former criminals - indeed the closest thing to a nation-like city-state is a group of outposts under control of Manuel DeZufingia - notorious drug cartel leader and father of a certain radio personality.
As to why Mexico has become more like 13th century France than Hellenistic Greece - its a matter of unfulfilled promise. Despite desire for reform from the 1910 revolution, each successive government generally only paid lip-service to the ideals, occasional a single leader creating a dynasty through puppet presidents.
None of this was improved by the masses of money and loyal - if informal - armies amassed by drug runners and other smugglers passing through the country.
However, one of the bigger points of contention was the drying up of Mexico's oil wealth, combined with the turmoil of the South Americas. Nuclear programs in Brazil, Argentina, Chile, and Venezuela presented not only technical competition of economics, but changed the past eighty years of strategic thinking, that always looked east and west for nuclear weapons - now there was a north-south element as well. New wealth, nationalism, and a change in the old status quo of economics meant a series of small wars broke out, and Mexico became all the more a strategic nexus.
Post event, many of the largest cities - especially the capital, became murder-yards. A number of the others are known to be heavily infested. Citizen presence is fairly low, though the north-eastern part of the country is home to some of the same group that has all but quarantined the US West coast.