Interesting how it's the basics that get us all riled up
It has been my understanding that twisting is what the code has had in mind for decades when they refer to "mechanically sound" and that solder or wirenuts are only there to keep them from springing apart from thermal expansion. That being said, if a wirenut is designed to be used for twisting wires, I don't see any problem with using it that way.
I was taught to pre-twist but I don't always depending on what kind of wirenuts I'm using. Traditionally shaped 72b and 73b sizes are fine for twisting, 74b and 76b not always. I don't use "reds" anymore - I've moved on to the red/yellow rubber coated Ideals which are waaaaay easier on my sore wrists for larger wires and they're very well designed for twisting wires. I was also taught to strip wire with my lineman's - now I use a stripper. I also use the stripper for cutting wire and cutting pretwisted wires since it leaves a nice, flat cut that the wirenut bites into better.
The one wirenut practice that I don't like is using tan wirenuts for any size wire. Yes, they grab a lot of sizes, but I think they look too OEM