While these phrases trace most obviously to the American constitution, they reflect values of freedom that any free society would normally embrace. When any of these freedoms are suppressed, then certainly, the values of any true democracy are undone, but also a strong set of biblical values. These are things like the dignity of human life, human expression, our pursuit of God and goodness; they could all be undermined.
And, when we talk of obedient nations, we are not necessarily idealizing democracy, since that form of government was not, in a complete way, really part of even any biblical landscape. But we've also seen in current global geo-politics, that democracy, as it's been played out in contemporary history, is certainly not a cure-all or necessarily every culture's choice of good governance.
So, we are not highlighting the values of an old, specific society as the standard by which to mark national greatness. We can at the same time see the preservation of this kind of stated values/ideals as a constancy in any societal health--whether in a monarchy, democracy, even oligarchy...--whether we're talking about the Western hemisphere, or the tribal societies in central Africa, the pre-Christian cultures of central Asia or the post-Christian societies of Europe.