I'm not a musician, but I would think that having a refined pallete in regards to musical tastes/knowledge would definitely aid an artist in putting his art into execution, perspective, context and could be a deciding factor in many ways. I've heard from a lot of bands and popular musicians that they aren't familiar with what is going on in their respective genre/scene and they want it that way so that their influences are pure and come from themselves rather then say, for example, making art that is subconsciously, unconsciously, or intentionally reactionary in the sense that the artistic creation is more of a product of it's environment or other external influences rather then pure artistic vision. Having said that, a lot of bands that do this surprisingly seem to falter, whereas some of the best bands out there wear their influences on their sleeves but do something different and original with them (the first albums of Darkthrone taking the Hellhammer/Bathory/CF style and doing something else completely new on the first few black metal albums while still maintaining those influences, brilliant).
To use another example from punk, I don't think the guys in Amebix have ANY idea what's going on in punk or metal the past 30 years. They released Sonic Mass and as pure and Ambeixish as it sounds at times, other sections of the album sound like fucking Disturbed to me. I know this wasn't intentional, as I don't think the Baron has probably ever even heard of Disturbed, but never the less....I still can't get into that album haha.
Burzum was another good example to use, he definitely has no idea how useless his current output is and that his time has come and gone, and other people are doing what he is trying to do now much more efficiently.