1) Did Blizzard ever stop to think that many (most?) people play their games as an ESCAPE from real life?
2) Anything on Blizzard forums goes on Google, and comes up in search results. That means anybody who uses their forums is going to be labeling themselves, forever after, as a nerdy computer game player to future employers, dates, etc...which is not something that is looked upon positively by many people. I would certainly discriminate against potential employees if I saw that they were a WoW geek.
3) People sometimes have bad days, say things they regret later...on a forum this is all saved forever. Luckily only the people who know their forum name can find it. So you protect your hidden identities more securely than you protect your email passwords. Blizzard aims to make all those mistakes unforgivable.
There is nothing that is possibly worth saying on the Blizzard forums that is worth sacrificing one's anonymity for.