Should our government promote any particular values?
Not electing criminals to public office?
Yes. Democratic, egalitarian, secular values.
Justice for all. Fairness in everything. Those are my 2 biggies.
On paper, we do, as @LiterateHiker wrote below. In deed, we have fallen woefully short from the getgo, and continue to fall short. The list of transgressions is way too long to list here but includes Native genocide, slavery, subjugation of women’s rights, Jim Crow, Vietnam, overthrow of Democratically elected governments in Latin America and the Middle East, and so much more.
Of course. From the United States Declaration of Independence:
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."
I love what President John F. Kennedy said about American values.