Interesting question. I routinely write wills that authorize the executor to destroy property that has no significant economic or sentimental value, but I've never encountered a case where a testator or testatrix has directed that property be destroyed and I've never seen a reported case (or even a news report) in which that has happened.
To the extent that an estate is solvent, there is no reason that a creditor could complain and if the destruction was done in a safe manner (as opposed to burning down a house or something like that without consulting the fire department) I'm not sure that there would be a public interest in doing so either.
There are many religions that had a practice historically of burying someone with grave goods, so there are reasonable First Amendment freedom of religion arguments for allowing such a practice if it had a religious basis.
And, if no interested party objected, I don't see how anyone could stop the executor from acting, unless the property to be destroyed was, for example, evidence of a crime, in which case it would be a crime to destroy it and the provision of the will would be void because it was a crime to carry it out.
If an executor sought permission from a court to carry out this instruction, the court might require a public notice of the planned destruction to give notice to any third party who might claim an ownership interest in the property allegedly belonging to the decedent.
On the other hand, usually, all interested parties in an estate can agree to act contrary to a will by unanimous consent, in which case no one would have standing to fight for the provision in court (unless it was considered a charitable bequest, in which case a state attorney general or an advocate appointed by the court with the "will" as the client could defend it). Given the strong public policies in the law disfavoring "waste" (i.e. useless destruction of property) such a provision could be held to be void as against public policy (similarly, bequests contingent upon marriage decisions are now void as against public policy).