It's for protectionism (though in practice the EU lifted existing domestic protectionist barriers on intra-EU flights whilst keeping them against outside nations)

Reciprocity is important here. If EU rules imposed no operator nationality restrictions (other than safety ones) on operating intra-EU flights, there'd be no reason for a protectionist US or UAE to negotiate deals allowing EU carriers to fly into their country at all, and those countries' carriers would be able to use their monopolies on intercontinental routes into the EU as the starting point to dominate all the profitable intra-EU routes from their European hubs too.