Teamspeak is only capable of loading ban lists up to 1 megabyte on the client. Also doing snapshots of teamspeak doesn't seem to store the ban list for me. It be interesting if we could keep track of ip's in sprum with reasons and even better if instead of banning them from TS they would be IP firewalled on the server. This is what i do manually currently as well.
For those unknown what this does. If you firewall an ip the banned user will simply not be able to connect at all. As far the users is aware the server is offline. It has in my situation kept many trollers and people from attacking my server as they think its offline.