Culture is really a slow motion war game. If you can make your films and music popular across the world, that will eventually buy you influence with the people of the world, and that in turn will turn into political influence.

That's part of the reason nearly every country spends taxes to support the arts/music/theatre/film.

By restricting foreign actors, you are restricting foreign countries culture spreading, and giving your own actors/filmmakers/musicians a boost. That in turn will translate into more worldwide cultural influence for your country.

To be honest, I'm really surprised all countries don't ban artists from non allied countries.