I have always assumed it is because forum chat is a written conversation, rather than an online letter.
Plus your user name is always displayed, so everyone knows who is 'speaking'.
I would always sign an email, in fact I always set them out as letters and use correct spelling and grammar. (Definitely no 'text speak'. I am only 41 but I get totally lost when people start using that!)
It would never occur to me to sign a forum post though....