http://en.m.wikipedia.org/wiki/Fort_Polk
Fort Polk is also a place to go.
It was also the site for the Louisiana maneuvers.
The LA maneuvers involved 400,000 men and were spread out over most of the state. Not limited to a base.
Practicing counter-insurgency on a base makes a lot of sense if you think you’ll be attacked there. If you think they are more likely to attack in civilian areas, you need to practice maneuvers where you will need to fight.
You don’t think they might learn something useful by having to deal with traffic, local LEOs, worried civilians, etc.? All of which they’d have to deal with during a real attack.