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

Do you have much evidence of them behaving irrationally?

It's a business not an ideology.

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