There are tons of dialog checks that are based on other skills, as well as your race, class, and background.
Yep, this. Certainly there are things that charisma checks can get you that other skills can't, but then there are things those skills can get you that charisma can't. Including barbarian-specific checks that provide unique solutions to some problems. Personally, I tend to use my player character as a face to get their unique dialogue and don't worry about charisma. And while higher charisma might give you better prices at merchants, it's not like money is so scarce that's worth speccing your party around.
Just go for whatever you think you'll find most fun!
