Whenever you see a government that doesn't have a significant organized crime problem, it's because either (a) the government is the organized crime (Russia), or (b) the government has resources at its disposal that are an existential threat to the organized crime while overlooking moderate operations (the US).
The US government has significantly overlooked organized crime operations in general (and while some members of government may have pursued them, it was largely a sideshow by the "legal" arm and not by the "operational" arm - and had organized crime retaliated against those senators, you can bet that there would have been an "operational" response). At times, we've worked with organized crime (running cocaine with the CIA, etc, or the CIA working with Lucky Luciano in WW2).
That's the thing with organized crime - it's not all that secret. So there's typically an informal balance stuck between the government and the criminals - don't be too much of a problem to civilians, and especially not members of government, and we'll leave enforcement to local law and not bring in the big guns, and we won't work with your competition against you.
I think the big difference, as others have noted, is that in Mexico there isn't significant corporate corruption in politics. So the money lining politicians' pockets was more likely to be drug related, and cartel specific. So the cartel wars extended into government and there isn't a sufficient corporate interest in stability to have pushed back against it. And well, now it's far past the point of a balance being stuck.
It's worth noting that we've had instances of significant local corruption and infiltration of organized crime into local police/AG/government in the US (including killing of local civilians by the police - you can search for "The Boys on the Tracks" - the argument against Dan Harmon is compelling) - it's just not as widespread and it's not at a national level.