FWIW, I had a similar impression of your comment as JohnMakin.
> give the friend a subtle clue that it's time to move on
If a friend needs someone to listen about life struggles and you tell them you're tired of it and don't want to hear it anymore, then you're not being a friend. Maybe you want to be encouraging and that is fine, probably helpful. But you immediately seem to turn that encouragement into threats of social exclusion:
> If that clue isn't heeded the friend often gets targeted 1:1 offers for help and can eventually just be shut out of the group altogether for being too negative.
I've seen this many times - people suggest "solutions" to something they don't quite understand, then get angry when people don't take their non-functional solution. Similarly, in online support groups, I've seen plenty of people storm off angrily because people are being "too negative", not seeing that sharing these feelings, wanting to be heard and knowing you're not alone with certain struggles can be part of a discovery and healing process. Those people use similar language you used in your comment of "misery loves company", essentially accusing people of wanting to be miserable and choosing depression.
If you want people to read what you write in a charitable fashion, refusing to explain the background for your comments is rather dysfunctional BTW. In general, people don't all have the same mental context and experience background to understand where you're coming from.