As you will know, the Iron Cross was around long before the Nazis.
I believe it dates back to the Napoleonic Wars (1813), when it was instituted as a gallantry award. It was always a battle award only, having to be re-instituted as every new war started. From 1870 to 1939 it had the reigning Emperor's monogram and crown as the center of the cross. The Nazis substituted a Swastika but they retained the custom of having the year the war started at the base of the cross. Despite appearance, it was still a military gallantry decoration only.
Many German soldiers and officers earned it during the Second World War for honorable service and did nothing to disgrace it thereafter. This included members of the SS. It was forbidden for German veterans of any Arm or Service to wear it post-war until 1957, when its swastika was removed and an Oak Leaf substituted.
Then there were people like Josef Mengele, who earned both lower grades I and II honorably on the Eastern Front. Mengele went on to become the chief medical officer at Auschwitz, and there are extant pictures of him wearing the EKI to give it its German designation while carrying out his murderous duties. He later escaped to South America and avoided justice until he died of a stroke while swimming.
It is things like this which make me hold the decoration in two minds, but I think the decision to allow it to be worn by veterans in the version with the Oak Leaf center was a fair one. One can only hope it wasn't worn by too many out and out criminals.