When you watch a great pianist, seeing her hands flying all over the keyboard at top speed and having no errors, you may think "Wow, she has great control!" It's easy to think that's the goal -- to achieve complete control over your movements. However, as with many other areas in life, things are not what they seem.
Conventional methods stress many hours of (tedious) exercises to, presumably, help the pianist achieve total "finger control." Unfortunately, these methods also create a very mechanical, stiff sound, and often lead to strain and other physical problems.
When you see a rock or jazz band jamming and/or improvising, you don't get the sense they are trying to control everything that happens. Quite the opposite; they are letting go and focusing on expression (communicating with the audience) and having fun. To do that, they must let go of trying to control everything.
When I have my students play a song by ear, even if they are not terribly good at it, they still seem able to go with the flow and enjoy the process. However, when reading notes from a score is introduced, many get very anxious and concerned about hitting all the right notes. I call it the "tyranny of the page." Consequently they start to do things which will actually make everything harder. In trying to exert control, the student feels he must "think about" every note he plays. Thinking is very slow, actually. If you think about each note, or what finger to use on that note, the playing by necessity will be slow and halting. Again, if you watch the master pianist, you will see there is no way they could be thinking about every note they play, especially if the piece is fast. ("Yeah," you might say, "but they thought about it when they first learned it." Not really. It's very hard to do one thing for years and then suddenly switch to doing something else.) Thinking, in fact, will undermine and counteract everything you are trying to achieve in your practicing.
You may notice that in hundreds or thousands or daily activities (tying your shoelaces, buttoning your shirt, climbing a flight of stairs, to name a few) you do them automatically. You don't need to think about the physical actions at all. And if you do think about it, you will probably mess up. (Think about where to place your foot on the stair and you may trip.) This is because you have developed muscle memory (which is in the brain, not the muscles) having done the same movements so many times. Thank goodness we don't have to focus on how to do these things every time.
The reason we do repetition in our practicing is to develop muscle memory. It lays down the "tracks" which your body will travel on the next time, and the next, and so on. Of course, mindless repetition is not good; it still needs to be focused (see my post on repetition, December 2023). Virtually everyone will develop muscle memory. It will be quicker in some people and slower in others, but it will happen. The body wants to take over and use the muscle memory it has developed. But if you start to think about what you are about to play, it interrupts muscle memory and renders it almost useless.
In addition to muscle memory, you have the power of the ear. Just like in singing a song you know, the ear tells the body what to do. It's more complex in piano than in singing, but the principle is the same.
If we didn't have muscle memory and the ear, no one would be able to memorize music, which, of course, people do all the time.
In the case of a few of my students, they are playing pieces for several weeks or months and still feel the need to look carefully at every note on the page to know what to play. By that point, the body should be taking over and relying largely on muscle memory. But the student cannot seem to "let go" and allow that to happen. They want to retain "control" by thinking. As a result, the piece stays stuck in the same stage indefinitely. They certainly won't be able to memorize easily, if at all.
Of course, if you're used to trying to control everything and suddenly you decide to try not to think so much, you may get a fair number of errors because it will feel new and unfamiliar. Then you may think "uh-oh, this doesn't work! I'd better go back to thinking about every note!" Thinking has become your comfort zone and leaving it can be scary. But you mustn't let wrong notes make you want to crawl back into the cave of wanting to be in control. With perseverence, the wrong notes will become less frequent, but the ability to be expressive will stay with you.
The excitement that the musician feels when he/she plays, and the excitement the audience feels, is a result of throwing caution to the wind and riding the wave of your accumulated skills and experience. Few people really enjoy a performance which is tightly controlled.