It's true, the 3-wire thread system is difficult to manipulate with a micrometer, but being a good machinist is developing skills to overcome this difficulty. I used to teach my students to do this manually by holding the wires in one hand, and the micrometer in the other while the workpiece was held between centers.
The charts in the PEE DEE set give you the reading over the wires equivalent to the maximum allowed pitch diameter; you can get the minimum allowed pitch diameter for any class of fit from the Machinerys Handbook. The difference between the maximum and minimum is the tolerance. There is no hocus-pocus about it.
If that doesn't fit your definition for a "precision screw thread", what does?
It's true, a thread plug gage does seem the only option for measuring internal threads. Machining a thread plug gage is a very real possibility if the part that you are threading internally has critical dimensions, or if you have a lot of them to do. I have seen a low melting point metal that can be used to pour in the internal thread, then screw the plug out and measure it with thread wires, or a thread micrometer. I don't know the name of the metal, or where to obtain it. I have never had any experience with it.
Don't get me started on threading, I could blander on and on.
Lord Byron