In addition to given an Amen to the comments of Erik Mead, Mary Malmros, Mary Eastland, Robin Boyd and Demetrio Cereijo, at risk of being obtuse, let me speak to training methods and effectiveness outside of martial arts with an example from my own experience.
In high school (many moons ago), I was an elite Mathlete. I even have a varsity letter and was named my high school's Mathlete of the Year. In other words, I was really good at competitive problem solving. 😊
A Math Team tournament usually consists of two parts. First, the players are given a challenging thirty to ninety minute multiple-choice test of unusual variations of the standard problem types. Then there are 16 to 24 single-problem written competition rounds called "ciphering" that are scored based on time (i.e. more points for getting the answer correct faster) or in order of completion of the competing players (i.e. the first four players with correct answers would score 4-3-2-1 and the remaining players would get nothing). In a tournament of twenty or more teams, scoring "firsts" or "seconds" is crucial to winning. The ciphering problems are either ordinary problems that would be difficult to solve quickly using standard techniques or are unusual problem variations without a standard solution technique. Both situations require the players to creatively apply the principles of problem solving to invent a fast and accurate solution technique in the competitive moment.
It requires a special kind of Math Zen to intuit and execute a solution technique under the crushing panic of that competitive time pressure. That Math Zen is not easy to learn or teach. It requires understanding principles, explicit confidence in the basics to avoid fatal errors and calmness of mind to avert the panic.
Mathletes don't complain that the techniques that they had spent considerable time learning were not effective in a competition. It is understood explicitly or implicitly that the problem variations and solution techniques presented in training were idealized versions designed to teach the principles of problem solving. Real, complex problems require application of problem solving principles and confident execution of the basic techniques.
I still regularly use those problem-solving principles to earn a very fine income as a software engineer solving novel problems effectively under the pressures of time.
For me, I feel/recognize that Math training in my Aikido training. If only my Aikido Zen now were as good as my Math Zen was then.
Explicitly stated, the lesson is that Aikido training is very much like Math training. Aikido training seems to be purposed to teach martial principles that can be applied to the world of general martial situations/problems.