How do you figure that?
Whats the circumference of a 13 foot diameter pipe?
I would use pi to get the circumference. Once you have your circumference, then you can figure out how far each degree is around the circumference of the pipe.
I worked in the industrial field for right at 15 years, and never once saw a blueprint with "radians" on it. That was let to the fitter to figure out. The engineer put what degree the pipe was supposed to be at, and I figured out the rest.
The quantity pi is fundamental, and any multiples of it are equally fundamental, so whether you want to use pi, 2pi 3pi/2, etc., as a fundamental constant, is pretty much semantics.
If you want to call "all the way around" 2pi or 360 degrees is again a totally pointless discussion, it is trivial to convert between the two. I can say that "all the way around" is actually 5 Farmers, in which case 5 Farmers = 2 pi Radians = 360 degrees. I can introduce arbitrarily many unit designations. Again, just convention and semantics.
Like I said, anyone that uses math for real life applications?
Wow, your bias truly shows. Science and engineering is not limited to looking at blueprints intended for fabrication or construction, nor is it limited to your field, whatever that may be. You are not the only engineer, and not all engineers do it the way you like to do it.
There is a difference between people who do, and people who teach.
I don't know exactly what you are implying by a difference between teaching and doing. Research professors who teach are first and foremost researchers, not teachers.
The physical laws that govern the properties and behavior of the things you are building were all written in a form where radians are natural (unitless), and hence they are unnecessarily cumbersome when represented in degrees. Different group of people, different standard. There is no better standard, there is no correct standard.