Music is subjective. Who exactly would judge "best musical creations"? If you go by popular vote, then only the country with the most people would win. Yes, people would only vote on the music their own country produces.

Also, in war, often it is fighting over something. Let us choose land as an example. If in a "music rock off", lets say Russia wins vs japan. Is japan just gonna give them a part of their country? I Don't think so.