The most important thing, in my opinion, is that putting effort into getting racquet tip follow whatever path or loop you think is proper, and particularly concentrating on getting that behind the back, is a flawed approach that will never get one achieve good form. I find it much more practical to see it as a "leave-behind" for the 90-deg bent arm holding a racquet while the shoulder starts moving around the spine and up.
I'm not suggesting a person try to hit specific points. But the points are important. You have to develop a feel for producing a stroke that hits those points. Some people, typically the very athletically gifted, can see a motion and reproduce it. Others seem to need a more structured approach. The end result however is what you suggest. One has to be able to produce the stroke from feel. Different people have different "feels" to produce the same motion.