I am the site administrator for the wiki. I will do my best to answer your questions.
The sole reason for requiring an account to post in the forum is to help reduce spam. About two years ago, a group of spammers discovered the forum and started posting in it on a regular basis. One of the limitations of the wikidot forum technology is that I can neither automatically filter out spam nor mass-delete multiple spam posts. The only way to get rid of spam is to manually delete each post, one at a time. This worked reasonably well for a while, so I continued allowing people to post in the forum regardless of whether they had accounts.
Unfortunately, earlier this year, the spammers became more aggressive and started making hundreds of posts on a daily basis. I remember one day in which they made ~1,000 posts, all of which I had to manually delete one by one, which took hours. With the open posting policy in place at the time, there was also nothing I could do to prevent it from happening again. I contacted the folks at wikidot and they said the only solution was to restrict forum posting to registered wikidot accounts, for two reasons. First, the wikidot folks have the capability to mass-delete all spam posts that come from a registered account, but not from a non-registered guest. Second, I am able to ban specific registered accounts from posting in the forum, which forces the spammers to create new accounts each time they want to post. I have banned 200+ spammer accounts over the past several months, about 3-5 per week nowadays.
By restricting forum posting to registered wikidot accounts, the spam has dropped substantially and I can deal with it quickly. However, I have indeed noticed the reduced frequency with which people now post in the forums, undoubtedly because they have to register a wikidot account. But I want to clarify that people with registered accounts are still anonymous. The only account information that is publicly visible is the person's username (which can be an alias, like yours and mine) and the date when the account was created. That's it. A person does need to provide an e-mail address when creating the account, but only the wikidot folks — not me or any other wiki users — have access to that. Moreover, when posting on the wiki itself, no IP address is shown for registered accounts, making them even more anonymous than non-registered guests in that regard.
Thus, I contend that registered accounts are anonymous, and they still permit the open exchange of information in the forum. However, people do have to take the one-time, simple step of creating an account; evidently, not everyone has been inclined to do so.
If I were to relax the forum permissions and allow posts from non-registered guests again, then I would simply be re-opening the door for massive spamming (the spammers are still around; this week I've deleted ~10 spam posts). If the forum doesn't seem very useful now, imagine how it would be if you had to sift through dozens — perhaps hundreds — of spam posts to find the legitimate posts each time you visit. I do not have the time to manually delete a ton of spam on a regular basis. Thus, I am reluctant to change things back to the way they were without an alternative anti-spam approach worked out. I welcome any suggestions from you and others.