maybe they can use other exchanges if it would take such a long time. A lot of countries accept this also between banks. So if you are verified within e.g. bitstamp or Polo (offcourse you need to be at verified level) and you send 0.00x coin to the new BTC-e then in a way you are verified and verifiable by law if they would have a case to check. In that case you would also stay anonymous for the new BTC-e.

Or maybe we should invent/use an ident blockchain for that. Sending out ID photos seem somewhat outdated in these days.