Here is an in depth article on Shu-Ha-Ri:
Takamura ha Shindo Yoshin kai
Its a little lengthy, but goes into detail about each stage, and the process it takes to go through each stage.
I believe the Shu-Ha-Ri process is more linear, though there is some back and forth. But, the three phases are basic phases of learning. When you learned to tie your shoe, you were taught to hold this string in this hand, and the that string in that hand. There was discussion about exactly where each string went, and how to use your fingers to manipulate it. After a while, you just tied your shoes... you were doing the exact same thing, only now you didn't think about it. Later, you started double knotting it, so that they would not come undone, or it became cool to use two different colored laces together, or you wanted to change the way they look, so you used different knots or your lace broke, and you had to improvise...
The Japanese system identifies these stages, and lays them out. But, if you learn anything, you probably went through this same sequence, whether you named the stages, or even recognized that there were stages.
There is a lot of misunderstanding about what kata is. I think a lot of the misunderstanding comes from people not realizing that it is only the first step. When people think kata is the sum total, they start using it to limit what they can do. Instead it is a tool that should be used to expand what they can do.
The traditional Shu-Ha-Ri method may not be for everyone. Other methods of learning may work better for different people. Not everyone may have the patience required to do the traditional Shu-Ha-Ri method. However, most methods (all of the ones I am aware of) include those three stages, though the arrangement may be different. Every time I have gone to a BJJ class, they demonstrate a technique. As students, we do the basic drill, step by step exactly as shown. Then we get shown little variations and we drill those. Then resistance is added and we do the proscribed technique despite the resistance. Then we roll. Most instructors encourage the students to try applying the technique they just drilled while rolling. While this may not be as formal as Shu-Ha-Ri... those 3 stages were certainly present.