A few remarks on your observations.
I would not say that the precision (specific value of the component) is what matters most, but most of the time the different technology used in the more precise component makes the difference. Many components such as resistors or capacitors are only 1% precise, but sometimes within a series fabrication they are precise to better than .1% and this does not make them better sounding per se. In my SoundLab speakers cheap good quality power wire resistors sounded better than the "creme de la creme" high power precision thick film ones.
Many great designers use low precision parts known for their better sounding quality, such as carbon resistors or capacitors using low precision dielectrics.
The 1704 DACs must be harvested and selected because they are not intrinsically high precision and in a DAC using the Trinity method of generating the wave this would distort enormously the signal. We can find many higher precision DACs, but they are not adequate to this job in the Trinity.
Averaging is just a good example we have alternatives to high precision.
Just wanted to make clear that although sometimes precision of parts is needed and welcome, it is not the unique way to get excellent sound or can be taken as an indicator of high sound quality.
BTW, before I see some eyebrows rising, we are using precision and accuracy indifferently - in science and technology matters they are two very different thinks.