I would advocate such a thing if I didn't think it could be easily turned on the US president or any of the other important leaders.
Leading powers would not be touchable by private armed forces, but there's a score of little ratbag tyrannies that could use a quick de-lousing.
The U.S.'s Logan Act forbids any U.S. citizens from participating in such an adventure.
The original 'filibusters' were a private army that went to Nicaragua in the late 1800s to do just that - quite a discouraging story, really. ;^)