Strikes me that if you publicly exclude cultural sites (whatever those may be) you'll get a bunch of terrorists hiding in cultural sites. Seems smarter to let it be known there's no place to hide.
Fighting with Israelis and other Western Nations, Muslims quickly learned that they could openly use Mosques and other 'cultural sites' as headquarters, staging, and launching sites. Essentially they would turn Religious sites, schools, and Hospitals, into functioning military bases. Because they know that Western Civilized people do not like to attack these sites.
Ironically, the Muslims themselves do not care one single little bit about stuff like that. When they are killing each other (which is pretty much all the time), they will turn a Mosque, Apartments, or Hospital, into rubble in only a few minutes. With no regard to how many non combatants and children they massacre, or whatever the 'cultural significance' of the site is. They simply do not care. Muslims fight war like animals, not like honorable, civilized, human beings.