Putting down your life for a cause and putting down your life for others are not necessarily the same thing. Take your soldier example for instance.
Lets say in one scenario the soldier leaves his loved ones to fight in defence of their homeland. They are putting their life on the line to try and defend and protect the lives of their loved ones.
In a separate scenario, a soldier leaves their loved ones to fight to eliminate slavers on the other side of the world. they are putting their life on the line to try and save innocents on the other side of the world, but their loved one is under no threat in this scenario.
In both of these scenarios also imagine the grief and sorrow of the loved ones if the soldier dies. In the first, they die for their loved ones, so their loved ones are alive and protected albeit grieving. In the second, they die for freedom, or to save strangers, putting that cause both above their own life and above the happiness of their loved ones. A loved one may by hurt that the soldier valued the lives of strangers over their own safety and happiness and relationship.
It's not unfair to say that both causes are noble and selfless, but humans aren't so logical as to not feel sadness or negative emotions simply because of selflessness. Wherever there's love there's always going to be grief, stress and worry. At least that's my thoughts on it.
No? It's not a bad thing. "Greater love hath no man than this, that a man lay down his life for his friends."
I think you may have a confusion of terms. "A martyr is someone who suffers persecution and death for advocating, renouncing, refusing to renounce, or refusing to advocate a belief or cause as demanded by an external party" Not all sacrifice is martyrdom. Some people are living lives of sacrifice, that sacrifice their lives not by dying, but by living in the exact opposite way that they wish they would, for the sake of others.
A nice deep question for this section of the forums
Well, I never have really watched Steven's universe to know all the cannon, and my internet is too slow atm to load that video but I would imagine it either is part of the character's mindset, or it's coming from the mindset of the show creators.