Remember that a private beta is only private insofar as it allows the core community behind a new site a little bit of time to get things set up without distraction. This small, initial group of enthusiasts need to come together and get some things worked out pretty quickly:
- What is on, or off topic?
- How are we going to tag things?
Of all the essential questions, those are probably the most essential during the private beta. If you don't get that right in the first week, it can be very difficult to fix later.
The good thing is this naturally happens as they begin asking and answering questions; if you bring too many people into these sorts of discussions, they tend to take much longer than they otherwise would. You need to have a degree of long term investment in the site in order to actively participate during the initial construction.
There's no reason why the rest of the world can't use the API to watch this happening, in fact some users have been known to find questions that they can really nail and begin composing answers offline in anticipation of the public beta.
Some private betas could probably have gone a little better if in fact they were just a little more open. You get cases where some proposals just take quite a while to reach this stage, where a respectable chunk of users that had once committed just lost interest along the way. There's also the case of folks not actively following Area 51 and missing the opportunity to commit to something that they're really passionate about.
While our often alluded "Area 52" should address the root causes of such phenomena, it also needs to have facilities so that those who are really interested in getting into a site early can do so, even if they unfortunately missed the metaphorical boat. We're fixing that to a degree in the current Area 51 model.
However, as I commented briefly below Tim's delightfully laconic answer, this behavior is very much by design. We didn't design the API to be able to be used as a spyglass into private betas, but we're happy that it does this. There's really just no reason to lock them down more than they are, and many signs indicating that opening them up a bit more would probably be quite beneficial.