Currently, when you combine the BP and Membership registration pages with the Membership add-on, there is no way to use default WordPress user fields in addition to BuddyPress xProfile fields.
First name, last name, nicknames ... these are critical.
I had to create a "name" BP xProfile field, which actually is not searchable in the user section. It is causing a lot of issues where my client can't find his members in the system.
I think it should be a core feature of this add-on to still be able to use critical user fields in the registration process, as after a user registers, there are default ways that WordPress searches them in the database, and we still need this.
Please let me know if this makes sense.