The Remain camp did a bad job of arguing the case because there really aren't that many good arguments for staying in. I think you'll find it was the Brexiteers

The Remain camp did a bad job of arguing the case because there really aren't that many good arguments for staying in. I think you'll find it was the Brexiteers that made the 'subtle points' about trade, constitution etc. Leave did have the advantage of some emotional pulls like sovereignty, but Remain had the advantage of all three main parties on its side (including a sitting government) and the very powerful emotional pull of 'fear of change'.