This would be a nice little feature but I don't think it would warrant the time we'd need to make it work. The mute buttons in the client are not tied to muting features that we have in our audio engine. So basically (as I understand it) we would have to make a separate mixing buss just for DJ Sona and implement an entire audio slider just for her which I don't think we can justify given the insane amount of work on our plates and not to mention all of the other audio bugs (like smite sounds when killing large monsters, Fog of War bugs, looping turrent lasers, etc.)
From a clarity perspective, we treat DJ Sona's music in the same way we treat Summoner's Rift music which is why they're on the same slider. Thanks for your post though - these kinds of ideas and requests get read and noticed and gets us talking and could help us design things differently in the future. Thank you Squeekems!