Naive question: If there are no such laws in the US, can one just simply store ALL personal data in Iceland?
From an enforcement point of view... if you have no EU presence, it'll probably be pretty hard for them to actually collect on the fines they levy, but as a director, travelling to Europe could be problematic. It's not entirely clear here, but it looks like there's a possibility of directors being held personally liable.
Far too many to even prosecute. But a politically active EU bureaucrat can just pick out key offenders to squeeze for publicity, piliticsl contributions, or even bribes.