That's exactly what I love about Guilty Gear's story. All the characters are unique, and have their own goals. Yeah a lot of them have strong ties with some of the others, but in the end they're individuals. It makes playing through every story fun, because even if the stories crossed at points, they were still different.
You can have a good time watching Sol hunt down I-no, then minutes later deal with Bridget's antics. It's a great way to handle story mode, keeps things interesting.