Well they could. Actually it won't be a big afford to clean up the servers. It wouldn't even keep support people busy once things are set up properly.
All Blizzard needs to do is run a few own public bots who simply record all clients and their messages. Then they only need to check for bot behavior, like repeated messages or catch-phrases (which can be done automatically once set up), count those occurences and finally auto-ban those clients for spaming after they hit a limit, i.e. 10 repetitions.
Really, it's not a big deal to do it; prolly 1 or 2 days for a skilled support guy.
"Hey Bash, how about it?"
[ Post edited by Dr.`disaster ]
Venture to the Realms Beyond to get off the beaten path.