Update: As of November 13th 2017, all Website fields and links in the "About Me" profile sections are unlinked on stackexchange.com, for all users regardless of their reputation on any site. We can thank the increasing spam activity on the network (a.k.a. The Great Super User Spam Invasion of 2017). So, in other words... this feature request is status-completed-via-the-nuclear-option.
This is one of those times when we overload terms. The word "network" in this case means slightly different things. A stackexchange.com profile is
- in a different database/codebase
- unaware of any site suspensions
- a "network" profile in name, but not really in the "your combined network profile that knows all the things about your per-site activities" sense
- informational only, so there's no such thing as a stackexchange.com suspension.
"Network suspensions" are just per-site suspensions with a certain reason. They don't currently notify stackexchange.com or update those profiles in any way.
With all that in mind, I personally would like to remove links from spammer profiles, but in practice this is probably more work than it is worth. Does anyone even look at these profiles? The practical damage potential here is very low.
And having said that, I solved this specific case with a network-wide deletion. :)