Why would you use it or not use it?
You're correct about the loyalty levels, they are regionally (actually county) based. The loyalty page here is just for mass changes. If the Union takes an entire state, for example Louisiana or Mississippi, quickly, then you can use this screen to attempt to quell statewide unrest quickly. For more regional or local changes, you'll use garrisons, generals, and armies to affect the levels. (Hint, generals with an occupation trait like Butler increase your levels significantly faster.)