We do so because we cling to this romantic ideal that the poor, oppressed civilians are helpless under the tyrant's boot - when in most cases, a sizable percentage of the population supports the tyrant (in return for a share of the spoils) and is directly responsible for his enduring rule.
I don't think it's possible in most cases to "free" a people from tyranny. Once we are gone, spoils-seekers will put a new tyrant right back in power. The poor goatherds who at the bottom of society won't have a say in matters either way.
If a nation threatens us, we should reserve the right to utterly destroy their capability to wage war. Short of that, we can only be a good example - and we could start by focusing energy on removing some of our own Federal tyrant class.
Your wisdom seems sound. Our unfortunate problem is a pretty hefty crowd of home grown goatherds kept deliberately poor and perpetually ignorant. The left has been effective. The right, less so, mainly because the right has been unwilling to accept the nature of the problem and to deal with it. What a pity.