testing trailer emergency brakes versus testing trailer service brakes

I don't think anyone is doubting your experience. Thing is, your experience is not normal. I've driven easily 100 different trucks, and I think I ran into 2 that didn't have a trailer brake.
Looking at pictures of cab interiors very few also don't have a trailer brake.

 

Almost none of the major truckload carriers that hire entry level personnel put trolley brakes on the instrument panel or steering column. They simply do not trust them to use them properly.

 

They did when I went to Swift. Admittedly that was 10 years ago, so.....

 

So, how are you supposed to know if your trailer service brakes are working or not if you don't have a trailer brake lever?

 

They simply do not TRAIN them to use them properly.

Also, how in the world are you supposed to do a tug test w/o a trolley valve?

 

Set trailer brakes, release tractor brakes, pull against trailer.

 

As usual, the manual was written by someone with little or no real experience driving a truck. He or she may have been involved in transportation engineering, or enforcement or some other tangential way.
A friend of mine graduated with a degree from one of only 2 universities in the US to have a degree program in writing technical manuals. He is 80 years old now. He wrote manuals for the US Navy on everything from how to use the galley ovens on an aircraft carrier to how to properly drive a tug while positioning aircraft on a land base. And things like an operational manual for a portable generator. He and his team would be given a subject, and with the cooperation of the manufacturer of the item would write a manual for the intended audience. Those of you in who have been in the military know exactly what I am talking about. Training materials and training films. He was a stickler for details and had to learn exactly how the device worked and everything that would likely happen if the instructions were written improperly. It is a very daunting task.
We learned how hard this was in 7th grade English class. The teacher said write out instructions on how to tie your shoes. 1. loosen the shoe laces, insert foot. 2.Snug up show laces from the front of the shoe. 3. Cross laces, wrapping one end around the other. 4. and so on. No one in the class did it correctly. Some didn't even remember to have someone put their foot in the shoe.
The OP is actually talking about 3 different tests. Testing service brakes. Testing Emergency brakes. Checking 5th wheel engagement(tug test) . So many of us have done all 3 so many times we don't think about it much. Think back to when you were a rookie when this was all new and strange.