In brief, no such thing as a "flag of convenience" ever arises. I'm not sure how this might arise, since smaller countries (Panama and Liberia) will benefit from having huge open registries. Since both of those countries are semi-puppets of the US, though, perhaps they come down on the practice prior to WWII? Then, during the Cold War, national security concerns keep countries from allowing companies incorporated in their borders from registering ships elsewhere, for the most part?
What effects would this have, both on global shipping and on anything else?
What effects would this have, both on global shipping and on anything else?