Just thought of a simple but great example... The scenario is of Good Guy and Bad Guy faced off at each other. Good Guy is right-handed, and makes a side step to his right. This does the following:
Fighting: Gives better access to the Bad Guy's chin line to throw a good right knock-out punch.
Shooting: Good Guy just "Got off the X" of attack.
Integrated: A 3 o'clock holstered firearm is farther from reach of the Bad Guy.
If you were just a fighter or a shooter, you might know one or the other. Taking the time to train in multi-disciples, and integrated training is where things like that come together and makes sense for several reasons.