What military assets are under their cultural sites?
Doubt Trump would blow up a cultural site without a good reason.
Building a missle factory under a cultural site, makes for an excellent reason.
If Trump destroys Iran’s Kharg Island petroleum complex it will set back Iran’s economy a decade or more. China, Japan, Pakistan and Malaysia would all have to look for new producers. The price of oil would rise and then stabilize as OPEC increases production. For that matter, present Iranian production is not all that much but the effect would still be substantial in Iran itself.