This is pure speculation on my side. But could it be that even though they were wedding presents - they (and e.g. the Oman jewels) were considered gifts to "the Crown" rather than gifts to Diana in person... and when she died the jewels then went to "the Crown" rather than to Diana's estate and Prince William and Prince Harry?

This could be an explanation to why we have not seen these jewels worn by the now Princess of Wales or the one living in California. If the Saudi jewels or Oman jewels were inherited by Prince William or Prince Harry... I am pretty sure at least the one living in California would have worn some of these by now... and am also sure the now Princess of Wales would have worn some if she had them laying in a safe at home...