The point is to gather feedback, expose areas where Let’s Encrypt still needs work (software and documentation!), and see how things scale both in terms of system load and stuff like community support.
Without a limited, private beta, the client probably would’ve had huge problems with a lot of common setups, and documentation wouldn’t be of any help. Community support and bug trackers would be overwhelmed. A lot of people would check out the project and abandon ship as soon as they ran into some kind of problem, which might have been caught in the beta. Now all of that happens on a much smaller scale with a group of technically-minded enthusiasts who decided they were willing to give an unfinished product a try and provide helpful feedback.