I would also like to see a bit more user administration options from the backend:

- Resending of registration emails.
- Manually sending emails to user

Also:

- Built in SEF
- Option to have profile URLS with the name of the user, e.g. www.domain.com/username
- no more additional css for cbb, take it completely from default Joomla css

Make image type field competely independent from avatar functions with own language strings, etc. so that the field can have different names and labels than the profile picture.

It would be nice to have a way to customise the backend userlists. Maybe the same way like you can make userlists for the frontend, it would be nice to have these functions for the backend as well.
With a large user database you could better organise and filter user based on registration and profile fields.

A feature to increase database security would be nice.
There is this PHP mycrypt. It would be great to have the option for each field, if it makes use of this PHP class. If yes, the field value gets stored encrypted in the database.
This would be great for rather sensitive information for not to be in plain text.

The core should come with those functions which are absolutely mandatory for a community solution (from my point of view):

Link to profile: www.domain.com/username

Better layout of registration page and profile pages with option for users to edit them as to their likes.

Similiar to this one:

www.joomduck.com/products/community-builder-profile-pro.html