That would probably be the best way to deal with them as far as the US is concerned.
No boots on the ground be they the US military or CIA/DEA. Nor any air assets like drone strikes. The US does not have a good track record when it comes to involvement in Central and South America. Like sure, the United States can absolutely crush the cartels' armed forces. All you need to see is how we dealt with the Taliban, Al Qaeda and even ISIS when it comes to open combat. Though, once they blend in with the general populous then we're shit out of luck*. Plus they're on the same continent as us. It seriously cannot be understate how having two large oceans helped the United States in so many ways... shit will just turn ugly with so many unintended consequences if the US start to swat the cartels. I hardly think the Mexican government can fill the void so... probably a non-state entity will take hold. And again, the US have a poor track record when it comes to replacing governments in Latin America.
* Seriously, the cartels and the likes of Al Qaeda and ISIS aren't that different. The cartels are just a business (I hardly see them wanting to actually rule as a state entity) while the likes of ISIS and Al Qaeda just have religious fundamentalism... theocracy spin to them. Al Qaeda produced a shit ton of heroin and the like. ISIS had their oil.
Edit: Also to any side that fights with US backing... don't believe the US lies. You'll probably be left dry in some way. Ask the Hmong, Vietnamese and the Kurds.