A government willing to participate in, and especially revel in, violence sets a precedent for the common people. It desensitizes them to the act and gives them an excuse that "if the government does it, I should be allowed to".
The government is supposed to reflect the moral and character of the society it operates. But it works both ways, and people (I imagine especially children) start to adopt the moral and character of the government - or an anarchic rejection thereof. So when you have Nazis, you get Hitlers Youth.
We should not be proud of executions. They are a dirty deed that "must" be done (though many would argue shouldn't - which I'm inclined to agree with after so many exonerations), so we should be ashamed and do it quietly, with shame for us and dignity for the victim.