This is a great tradition and one that surely helped the fighters to perform their best. Remembering that they were mortal was also a great way to help keep these generals from thinking too much of themseleves and taking control and issuing orders that they did not really have the right to do.
The human spirit is not indomitable. Everyone has their own free will. Slaves may seem like they are being subdued and act defeated, but they do have a choice. They can run away if they chose to, even though they may be killed or punished, or they can stay and do what they are told. Even the victorious generals that are under no control are not indomitable. They have the choice to make people slaves, or they can be nice and let people live how they want to. Every human spirit is able to make it's own choices, whether they like the choice they make or not is how they perceive it.
Even victorious Roman generals had their spirit beaten down at multiple points in their lives. While the urge to continue rising and fighting is part of the human spirit, the spirit itself can certainly be beaten down and defeated, if only temporarily. The Romans understood that the high from the adoration of the crowds is also only temporary, and used this method to "ground" themselves.
For the most part, people are quite resilient. When things go wrong, we typically find a way to work things out another way. The human spirit is not completely invincible, however. Given enough pressure and lack of support, sometimes the human spirit is crushed, as we see when human beings crack under torture or commit suicide. This is rare and difficult to see, but unfortunately it does happen.