They'd probably quickly stop cheering as their own homes and families were destroyed as collateral damage, which is what would happen if the "full force of the US military" were deployed against the cartels.

We were briefly greeted as liberators in Iraq too.

The destruction of cartels would involve careful policing and corruption controls, the best American administrations have been bad at this. The worst... can barely put its pants on much less dismantle foreign organized crime. You can't shoot a missile at a cartel and poof it's just gone.