Possibly the reason he could destroy the wand was that he was its 'master,' (for those who don't know a large plot point in the final canon book and movie was that wands have particular masters that they are bonded too, and so can only be wielded fully by them or someone who defeats them. Hence why Voldemort couldn't use the elder wand properly. )

Presumably having access to all the wands power as harry did at the end would allow one to override the safeguards against destroying it?