Neither private constructors nor abstract classes were defined in the old ECMAScript 4 standard on which ActionScript 3 was based. If I remember correctly, the ECMAScript Working Group chose not to implement these more complicated OOP features because there was a certain focus on simplicity and backwards compatibility with older versions of ECMAScript. I interpreted what I heard from them as "we may add these features later, but let's take it slowly". The abstract keyword, for example, is a reserved word, so they have this stuff in mind.
It's worth noting that the working group has chosen to restart the next version of the language with a new focus. This effort is called "Harmony" because two rival sub-groups had very different opinions about where ECMAScript should go in the future. It's a bit of a compromise. Harmony is going to progress much more slowly than the old ES4, and even the class syntax that was already implemented in AS3 will be dropped from the standard initially. In other words, they're going to keep it looking a lot more like today's JavaScript for a while to focus on some other features that are important to the group that was going to branch. This will become ES3.1. Later, classes and some of the more Java-like OOP features will be reconsidered for a new ES4.
What about AS3, though? Basically, Adobe jumped the gun by using a standard that wasn't yet complete, and they got bit by politics. However, Adobe intends to stay involved with the ECMAScript Working Group, and they will likely consider adding features that the working group recommends. That said, AS3 may never be a complete (or fully compatible) implementation of a future ECMAScript. What does that mean? Well, since they're non-standard again, Adobe has the option to add features to ActionScript, even if those features aren't part of a standard. If you feel abstract classes or private constructors are important to you as a developer, request these features in the public Flash Player bug database, or vote for existing feature requests, if they're already present.