What do you mean by "critical mass"? Private betas have very few users intentionally. The aim is to quickly build a solid foundation for the scope of the site. This is done by members who participated in the definition or, at least, saw it on Area 51. Hopefully these people know what they're doing or at least are trying to create a good site. People invited later would be quite a different class of users.
Private beta normally only lasts a week. If the site isn't ready at that point then measures are taken to evaluate whether the site can succeed and to work out the issues if possible. Inviting more people who previously knew nothing of the sites internals would probably be disastrous at that point. It's like piling more developers onto a late software project.
In any case, the point is not for the site to "incubate faster". It should incubate well.