Dedonta, first of all it is not generally an unmodified courage check - the -1 for enemy within 6" applies quite widely.
Some lists basically ignore courage for practical purposes. For example, my Ithilien (Gondor) list has recourse to Faramir's auto-pass, heroes with 'bold beyond belief' and 'Inspiring leader' heroes with courage 5 and 6. For them, even a failed tist is just met with a shrug, they will pass the next time around and the rest of the army will pass theirs.
However other armies really dread the courage tests. I hate them with my Carn Dum (Angmar) army. The troops have a base courage of 2 a single hero with Courage 5 (who will be passing his tests) and then an Inspiring Leader with a mere courage 4. Thes guys are in big trouble when they hit situations with a -1 penalty to tests. The Wraith's unit is probably fine, but everyone else is effectively courage 3. Courage 3 fails 15/36 times. WIthout the leader, they will be courage 1 once you take into account the penalty. Courage 2 fails quite often even without it....
In that case, once they lose combats, 5/6 of the time they will very likely not pass a courage test next turn and if so will be unable to move or charge and get only 1 dice per coy in melee. That is, they are screwed.
The situation for them could be made worse still with Dismay magic, or units forcing them to pass terror tests, but you get the idea.