Its interesting John, that you are just becoming aware of tools from general industry, hole / bore gauges have been around a long long time.
You may be interested to learn that not everyone has the machinist background that you have. My experience has been primarily in music education and saxophone performance, and so while I am familiar with the larger "T" gauges, I had not seen the small hole gauges before the clinic I attended.
Why does anyone need to know exactly how open a pad is
There are many answers to your question, but just let me give a few off the top of my head.
- When a proficient player's saxophone comes in for an overhaul or repad and the player is happy with the tone, pitch, and response of his/her instrument it is important to return the venting of the toneholes to exactly the same specs as when the instrument was brought in.
- When a proficient player comes in to have the keys opened more for whatever reason, and then comes back two weeks later and says he/she liked the sax better the old way, it is important to have taken accurate measurements and kept good records to restore the keys to their original positions.
- When experimenting with key heights for overall intonation and timbre as with any scientific study it is very important to have exact measurements to compare changes in venting with changes in pitch and vice versa.
- When a manufacturer such as Yamaha gives factory specifications for the key openings of its saxophones, it is important to have the correct tools to set-up a saxophone to those factory specs when asked to do so by the customer.
Certainly not all repair techs would find the above interesting or even necessary. I am one who does. I hope this answers your question.