Disdole This would have been a better question to ask, as there are other solutions than removing the password requirement.
What you're looking for is guest posting, allowing an unregistered user (or a single, 'guest' user with the username/password publicly known), to post.
You would likely need a new extension for that, or a cron job on your server which resets the password of the guest user ever X hours to keep it available. You might want to look into this existing topic on the subject of anonymous posting to add your support.