I think anonymous posting has benefits and it would hurt the boards to get rid of it.
The problem is the kind of anonymous posting that is allowed. If you go to a site like Fark.com, there's a lot of robust anonymous posting, but it requires registration and a 24 hour waiting period before you can post. This keeps people from posting under 1000 different names and lets the mods ban people who just trash up the board and annoy other posters - like some of the political posters on here with 1-track minds - even if the ban is just for 24 hours as a cooling off period for bored high school kids. There are ways around this but it would keep the volume of annoying crap down.