Banned user status: visible Vs. invisible

I can't help but wondering if this question was inspired by this recent question on Meta Stack Exchange: Why are current user suspensions visible to other users?

I'll rephrase my answer from there because I think the reasons (for the ban to be publicly visible) apply on other communities too:

• Deterrence; when you're reminded now and then that bans are real, you'll be more inclined to follow the rules.
• Transparency; it's good that you can see that a user whose suspicious behaviour you've reported to the moderators/site owners serve their deserved penalty.
  • The community/system might have other ways to report this back to you.
• Preventing confusion; yes, a one-week ban is almost indistinguishable from a one-week vacation, but it's still strange to see a user not responding to your posts / comments / chat messages when 1) their profile says they've been online in the last hour, or when 2) they were seemingly very interested in the discussion. This will only lead to speculation.
  • An option here which helps for 1) but not for 2) would be to not update any 'last visible' indicator in the profile.

An argument against showing the ban would be that nothing on the Internet can be permanently deleted; if somebody saves a banned user's profile in the Wayback Machine or other archiving sites it's going to take quite some work to remove it.