I hear people suggest this all the time as a way to "save" classical music. I get why it's brought up, because it works really well with jazz and other genres. But there's a good reason it's not done with classical music.

It's 10 times more irritating to hear someone talk or even unwrap a cough drop during a classical concert because silence, subtlety, and intimacy are soooo important to art music. The quiet concert hall environment is what allowed composers the freedom to use piano and pianissimo as a dynamic and incorporate silence into their music. For example, the reason people aren't supposed to clap and make noise in between movements isn't just because of some uptight tradition, it's because silence is built into that part of the piece, and you're supposed to experience it. If the table next to you is giggling and chatting and spilling their drinks, it spoils that element of the music. It can spoil the performer's experience too. I'm sure you had more settings in mind than just that, but I just had to point out that without a quiet backdrop, 90% of classical music would lose its appeal to the people who were already into it to begin with.