@AC
"Surely .eu identifies the continent, not just countries in Europe who belong to the European Union."
I dont know which the .eu is intended to identify and I dont really care (this TLD stupidity being just that). But it does bring the question of what the EU identifies as since it regularly mistakes itself for Europe while actually being a political union inside but not wholly.
Remain or leave the TLD argument is just the EU shooting itself in the foot. There are better implementations of taking back the domain names if that is worth more to the EU than the money.