It irks me a little when closed captioning just says, "Classical music playing," during a TV show. I always think, "All Classical music isn't the same. Gershwin's 'Rhapsody in Blue' isn't the same as Victor Herbert's 'March Of The Toys.' Identify the composer and the piece! That'll give more people who don't listen to much Classical music a chance to seek out a piece and buy a recording of it. While you're at it, identify the orchestra and the conductor, as well. Tempos and stylistic interpretations vary widely sometimes, so someone who wants to hear to that exact version of the piece should be able to purchase it."
The arts always need and deserve our support, especially during a pandemic. Identifying any piece of music playing in closed captioning couldn't hurt.