All true and very good points, especially when doing drill based training. Train slow, learn fast. But there is a time to test what you learn and that requires faster speeds and greater stress. The question is what percentage of overall training needs to be 'testing' as compared to 'learning'?
I think that you are testing at the same time as you are learning. Take, for example, the simple push test exercise. You stand with arms extended out to the sides. Someone pushes on your open palm. As you start learning this exercise, you are testing your body with how much force it can "ground". As you progress, you find yourself able to structurally hold up under greater force. As you keep going, you find yourself learning to hold structure under a force that goes through you, up at a 45 degree angle, around you, etc.
You're actually testing yourself as you are learning to build structure. Start playing with a technique and you find just where you can keep structure while moving and under a load/pressure. Keep working that, and you get better at things.
Keep working all of these and you find that you can move quicker while still being able to hold structure under movement and load/pressure.
You're testing yourself each and every time you work on this stuff. The better your structure, the more you pressure test it. The more you pressure test it, the better your structure gets.
The hard part is not to overload yourself because you think you should be able to do more or should be better at it. Not to go fast to gloss over weaknesses. To work on solo training.
Does that answer the question?