"Does this seem to be an abnormal way to train for self-defense?"
I wouldn't say it's abnormal, but it can be counterproductive. In a face to face, life and death encounter, your stress levels will be through the roof. You pulse will be 200+. Your eyes will not focus. You will forget to breath. You might pee in your pants. Your mind will not function normally. What you will do in that situation is your training. If you fire one shot and re-holster in training, that's what you will do in a self defense situation. If you draw and do an instant, point-shoot double tap to the COM, that's what you will do.
Also practice your visual focus. Forget your sights, you will NOT use them in an up-close shooting. Practice focusing NOT no a whole body or target, but a small dot on it. On an individual, that might be a button on his shirt, or his nose.
I know it sounds strange, but it's true. Ask anybody who has actually done it. That's why it's so important that your training exactly duplicates what you want to do in a gunfight. Under the intense, crushing stress of that moment, for better or for worse, you will follow your training.