i've came across many stupid ideas, but would never put distortion on master buss. :D
the main problem with majority of free distortion plugin, or at least the ones I've tried during the years, they act more like fuzz, than kind of overdrive/saturation. Fuzz adds plenty of noise to the source material, which personally I dont like,.
For subtle distortion I ammainly using all kind of tube saturation plugins. It servers well for the purpose. I got much better results than if I would use distortion plugin.. When you twist them hard, you got very nice distortion edgy sound, but it doesnt break up, and doesnt turn into brittle noise all over the place as it is very often with free so called distortion plugins.
Just came to idea, what happens if you would add slight amount of distortion, as send fx on you master buss or just subtle amount during mastering, but only on Side part of signal.