You can set your username to whatever you want. I do! The issue with /user/username is usernames are not unique on SE and it would need a massive re-design of how we think of profiles.
Your profile is actually linked to your userid (and in DB terms that's pretty much your primary key), and your user name is something changeable (every 30 days cause some people abuse this and we can't have nice things because of this) at any point.
SO you already have a vanity profile name (and I set my "real name" to Firstname "Journeyman Geek" Sirname - cause no one would recognise my real name), and a real name field you can set/change to anything.
Displaying your username as /user/vanityname is implausible since there's no constraint on that being unique and that's going to break a ton of accounts if changed.