You are telling me something as informative of our identities and who we are as sexual identity and gender identity can be picked on the fly and it doesn't in any way effect how the character interacts with the world other than who they fuck isn't a blank slate?
In the real world sexual and gender identity are not a choice. In works of fiction those things are inherently a choice by a creator, video games are just one of the few mediums where creators can give options to people. I don't think that giving people those options should necessarily mean weaker character writing.
And I guess when I see blank slate, I think of games like the Fallout 3 where the created main characters barely emote, or silent protagonists like Gordon Freeman. While characters like Kassandra or Shepard feel like they have more personality to them then most set characters in games. I wouldn't describe either as "soulless".