> When the Bamiyan buddhas were dynamited, exactly whose culture were the Taliban "preserving"?

Their own.

> It is entirely reasonable to believe that culture and history have an importance independent of petty, local squabbles.

Calling it “reasonable” elevates it to a level of objective neutrality to which it is not entitled. That view is simply it's own set of cultural values, which, while perhaps fairly widespread at the moment, are no more universal or grounded in reason than any others.