Yes, the government should do more to spread the word about Carpenter's inspiring story. He stood in front of a military insurgent attack in order to shield another soldier, and in doing so, probably saved the other soldier's life. People should hear his story so they can express gratitude for what he did for us.
In a world where heroes and inspirational people are not always easy to see, more should be done to promote those who have achieved heroic deeds during their life, in order to set examples for future generations. More should be done to tell the stories of everyday heroes also, and promote kindness, which is a rarity these days.
Being awarded the medal of honor is a huge accomplishment. If I remember correctly there are only a handful of people who are actually awarded the medal while they are alive. I think his story should be all over the news to talk about how great of a hero this man truly is.
I do not believe it is the governments job to push out stories about our military personnel and their struggles. As a community, as a country, we should do this on our own. The government is in place to handle funds, redistribute them, and take care of foreign policy among other things. The government shouldn't be seen as a PR company for injured soldiers. With that said, Carpenter is truly a heroic man and he deserves more recognition beyond a medal.