It's not that I want it on non-problematic members, but if someone is banned from trading, it should be known so people can't trade with them. The group prevents them from Marketplace access, but if a user banned from trading were to send PMs, there's nothing stopping an innocent receiver from trading with them.

While I would think someone banned from trading should just be banned as well, are you saying Alexx should be banned?
Or should the banned from trading group be removed altogether, which would then allow Alexx to trade again?