The disadvantage is that since objects cannot be relied upon to have a 'default' (parameterless) constructor (which would defeat the purpose), you would have to remember to explicitly invoke the super constructor with all applicable arguements, every time. I don't see this as being terribly more convenient that having to write a new factory method.
Then you have sloppy code with dead limbs hanging off of it. Because the old Factory function is included in the new object along with the new one. *Code Bloat*.
There's nothing wrong with writting a simple line of code to call the base constructor. C#/Java programmers do it all the time.