The pre-Crisis Superman did have a problem with women and a fear of commitment. He also has a problem with letting go of the past. He kept his parent's house for years after they died. I think he still had it by the time of the Crisis. After Kandor was enlarged, he had a replica built and put on display in Kando's old position. He actually has two replicas.
The thing is, Superman's fetish with statues and replicas is really about the artist wanting to draw cool and iconic stuff. Same for the Batcave museum with Jason Todd's Robin costume, the dinosaur, and the big penny. In any real-world context, such things would be creepy indeed, but do you count a trait that a character has for strictly visual purposes as a flaw? It's like the litany of villains who have "must discuss their plan in great detail". Would they really be that talkative in the real-world, or is that a device so you can have a word/thought balloon to set up a scene, a concession to the medium?