I think that it wouldn't have been wise to open Diana's apartment to the public, particularly soon after her death. Diana's most devoted--to the point of hysteria--"fans", from what I've seen, can idolize her too much. There was probably real concern about her apartment becoming some kind of a shrine or being overwhelmed by the number of people who would have wanted to see it. Also, I've noticed a tendency among the most radical of Diana's "fans" to have an anti-monarchist view--to the point of thinking of the Windsors as evil, and I think that the historical royal buildings such as Kensington Palace could be a target for vandalism. Sure, there's security there; but when there's a large number of people in one place, things can happen.
By "fans" I'm not referring to people who were interested in Diana and were fond of her; I mean the people who were on the "fringe."