We would do it with the cooperation of the Mexican government; overtly, covertly and/or tacitly.
Still, I agree; taking down one cartel will simply create a power vacuum to be filled by another.
However, what it would do is give a very sharp lesson to all the Cartels: Don't fuck with innocent American citizens.
Americans going to Mexican to make drug deals get what they deserve. People who look for trouble usually find it. These Americans were innocent. Note, too, that one innocent Mexican citizen was murdered too in the crossfire.
While eliminating the Cartels is unlikely, keeping them in their lane is entirely attainable. This particular cartel will be made an example of by both the American and Mexican governments.
A few years ago a couple of enterprising punks started mugging American touristas on the beaches of Cancun. Those hotels are where the Cartels launder their money. The number one rule there is "Don't fuck with the Cartel's operations". The punks ended up with their heads inside ice chests outside of town.
If nothing else, the US and Mexican government can have the other Cartels take down the dumbasses who murdered innocent people.