I never noticed that normal users don't see the suspended badge... The only community where I see many banned profiles is here and I'm admin so never gave it too much though.
While maybe unrelated, I find the lack of ban reason a bit disturbing. We probably don't care about spam bots, but for normal profiles being banned it would be great to be able to give a little message. The reason type could also be something made public "This user was banned for spam", or things like that.
I feel like it's rare to see banned profiles. Most are spam bots, and the discussions they create are usually deleted. So no one will see their profile unless there's a public user list. Only for normal users that don't have all their posts deleted it might make sense to show it's a banned user.