I don’t think the technology matters nearly as much as the asymmetry. Iraq had better technology than the Taliban and their military didn’t last a week.

How are they not rational? Violence is a tool. They operate an illegal business so they can’t sue other parties for breach of contract. They can't call the police if they are robbed or file an insurance claim for what was taken. Even the over-the-top violence has a rationale. They aren't punishing the victims as much as they are attempting to broadcast that there is a higher price to be paid than any gain from giving information, to reduce their future losses and enforcement efforts. It isn’t moral or ethical, but I wouldn’t say it is irrational.

The cartels are incredibly rational - what they lack are morals and ethics

It's a business not an ideology.

Do you have much evidence of them behaving irrationally?

I would recommend reading the Freakinomics book or listen to their podcasts on drugs.

TL;DR: drug cartels are run like businesses. They are very rational. But, unlike your boss, their boss can also shoot you in the face if you annoy them too much

I think a lot of people would be cheering on the destruction of the cartels.

A non-aligned population will look out for their own interests and are aware that the attention of the US is temporary but the cuadillismo that lead to cartels are a durable cultural artifact.

  The Battle of Culiacán, also known locally as the Culiacanazo and Black 
  Thursday, was a failed attempt to capture Ovidio Guzmán López, son of Sinaloa 
  Cartel kingpin Joaquín "El Chapo" Guzmán, who was wanted in the United States 
  for drug trafficking.
  
  Around 700 cartel gunmen began to attack civilian, government and military 
  targets around the city, despite orders from Ovidio sent at security forces' 
  request. Massive towers of smoke could be seen rising from burning cars and 
  vehicles. The cartels were well-equipped, with improvised armored vehicles, 
  bulletproof vests, .50 caliber (12.7 mm) rifles, rocket launchers, grenade 
  launchers and heavy machine guns.