I’d rather have some kind of in-game mission/objective for my character than for them for to be a completely blank slate. Right now the PC feels sort of lifeless. All the companions have something they are working towards, but the PC is just kind of there.

If you didn’t want to pursue their personal quest, you could just ignore it or maybe even have an option to turn it off. I also think you could make them general enough that they fit a variety of character types.