What did the mercenaries have to do with the decline of the Roman Empire?

The Roman Empire was built upon the basis of supreme military discipline and training. However, as the empire over-extended itself and split, the Western Empire could not afford its superior army anymore. As a result, it began to use mercenary armies, usually filled with barbarians. Therefore, the armies were not that disciplined and had no loyalty to the Empire; logically, the military structure fell apart. And once that happened, the political structure fell apart. Often times, the mercenary armies would turn on the Romans and began to demand/seize land for themselves. For instance, Alaric, the Gothic king who finally captured Rome, was originally a mercenary leader for them.