Obviously there is a tax angle here, at which point the tax authorities should care about your chicanery, but I wonder because, even if it isn't realistic to make "mistreatment of art" a civil or criminal liability, you could make it into a social liability.

If you destroy art, or squirrel away an undue amount never to be seen again, or what-have-you, and in return, a number of prestigious artists and art institutes could decline to have anything to do with you. You could no longer serve on the board of the Met, and your donations would be refused. Artists would refuse to sell to you or accept commissions. I suppose it would be counterproductive to stop accepting loans of art to exhibit in the museums, but perhaps they would only be accepted to exhibit anonymously -- no "on loan from Big Wig collection" next to the painting.

This probably wouldn't work if too much of the money that flows to artists and art institutes comes directly from the pockets of billionaires; I'd be surprised if, on aggregate, even principled people would be willing to cut out more than 5 or 10% of their income as a matter of said principles.