That was the point of my second example. Sometimes you can’t tell why people aren’t playing on OGS at the moment. Is it because they’ve been banned or is it because, say, they’re busy in real life at the moment, or they’re sick or something.
If it’s just some random account that you have come across then, yes, this is akin to gossip but if its someone you’ve personally played multiple times and enjoyed playing then, no, its not akin to gossip.
Personally if I ever fall sick and have to stop playing on OGS as a result, I won’t want it to be displayed on my profile. Apologies in advance to everyone who’s enjoyed playing against me.
It’s still a bit borderline. If you (whoever) have a way to contact them outside of OGS then you (whoever) can still find that out. If not, and they become inactive, probably in most cases you still gain no information as to why they stopped playing on OGS other than “they weren’t banned because otherwise there would be some label”.
Still it’s not clear having such a label is useful even then. For example, suppose someone gets banned and then later successfully appeals, I don’t think one needs to tell every passer-by on OGS or everyone in that player’s friend-list why they were banned.