If a stored property is private, it's assumed that that field isn't one that other files should know about. That means that the memberwise initializer can't advertise its existence.
That said, the deferred memberwise init proposal includes the ability to declare the initializer and specify the access level explicitly while still having a synthesize implementation. I'm looking forward to revisiting that if / when somebody is willing to work on a prototype implementation (I don't have bandwidth to do it myself).