The idea behind this is to make it easier to check if unwelcome users are signing up again (e.g. tuxamd/1U). A list of IP addresses to look out for could be created based on the users posts, and if someone signs up with that address the moderators/admins could be notified somehow, or maybe it could be implemented as a sort of 'Watch this IP address' functionality like the new 'Watch this User' we've got now.
There would probably be a fair number of false-positives, but this could make it easier to check that banned people aren't coming just creating new accounts.
We might also be able to take advantage of phpBB's built-in ability to require all new accounts to be activated by an admin, except modify it slightly per maedhros' suggestion. (i.e. only matched IP addresses get flagged for admin activation)
Looking at the posting history of some problem users we've had, they have enough unique IP addresses that it might also be useful if we could manually define blocks that should be flagged for admin activation. Ideally, these blocks would use CIDR to give us all the control we want/need. (i.e. 192.168.0.0/16, etc.)
Another semi-related idea: would it make sense to check IP addresses used to register accounts to see if they've registered more than N accounts in the past Y hours? And, if so, either deny it outright or flag for admin activation? This might help against spambots.
Fixed and live.