It would be really nice to be able to hear the ready up sound for competitive while "alt-tabbed" for us single monitor plebs who like to watch a video while we wait for a game to be found. A good example of this is CS:GO's ready up (I should also note it should be loud but not ear bleeding loud)

You can already do this!

Just open up your settings menu and under the audio tab you should see an option labeled "Sound in Background"

When that option is checked, your game audio will persist even when alt tabbed, meaning you can hear the ready up noise when the game is not in focus.