If it was a competition between broadcasters, then the UK would have at least three entries - BBC, ITV, and S4C. I bet it's the same in other countries, multiple broadcasters being EBU members.
The Champions League is a competition between football teams from within UEFA however there are hundreds of teams that aren’t in.
Of course it’s a competition between nations, but each entry is put forward by a broadcaster. So it’s both a competition between countries and broadcasters. Of course using the nation is an easier way of selling something to an international audience than the name of a TV brand they’ve never heard of.