I can't put my finger on it either. It's a bit like in "Rebecca" where Max de Winter orders Rebecca's bedroom to be shut up after her death. His new wife believes this is because he will never love anyone else, and is encouraged in this delusion by the sinister Mrs Danvers.
At the end of the film the truth comes out when Max says to his wife "I didn't love Rebecca - I hated her!"
I'm not saying Richard hated Anne

, but I venture to suggest that such overelaborate displays of grief (e.g. destroying her apartments) might mean that there were some other issues that had never been resolved within the marriage, and that he was still "haunted" by her. Maybe he felt guilty about something?