Sadly enough the first thing I thought of was what if pirates take control of one these ships? Now a bunch of armed bandits are holding a nuclear reactor hostage at sea. There is even some incentive to never return it but disassemble it and sell it to terrorist organizations.
This will (hopefully) never happen. The Egyptians will surely not let a 100 nuclear reactors sail through their country every day. But maybe they will and the next Evergiven will be the Everradiant.