There are many reasons for having an open forum.
Although there is higher upkeep on an open forum, there are majour benefits for it. For example, if someone was browsing a support forum, and just happened to know the answer to the question off-hand, do you think they will really take the time out of their day to register, confirm their email, then post their answer? No, chances are they are just going to leave the question unanswered and not bother with the trouble.
By locking out people who are too lazy to register their support requests, you’re also locking out people too lazy to register to save you work and answer support requests.
Someone has written a whole essay on the benefits of anonymous (“open”) posting: http://wakaba.c3.cx/shii/shiichan