> Imagine the impact on an HPKP site.
I don't see why the impact on a site using HPKP would be different than for any other site. In both cases the site would have to install a new cert.
The only difference with the HPKP site is that they'd need to make sure their new cert uses the same key as the old one. (Or they could use a backup key/cert, which I'd expect them to have anyway if they're using HPKP.)