Long ago, in a land far, far away, Kanye West put out an album called 808s & Heartbreak.
At one point, he released the stems for the track Love Lockdown to be remixed by fans.
While not really in-line with my regular choice genres (though I somewhat dislike genres),
I dug the album and downloaded the stems. As I recall, the producers implemented this technique.
One track dry vocals, second track distorted vocals.
That sticks out in my mind because it seemed so strange to me at the time.
Something just occurred to me, though. Sure, you have wet/dry controlls... but what if you want to affect the distorted signal further?
It wouldn't be possible to do so in a chain without affecting the dry signal as well, 'ew see.