Good movement begins with an awareness of your body. How you’re feeling today, sensing how your joints and muscles feel as you move them, and especially an awareness of where you weight is and how your body is positioned.
If you've got a good coach, they can cue you to get into good positions and bring your awareness to weaknesses in your form, but only a lucky (or perhaps unlucky) few have someone around us all the time to act as our checks and safeguards of posture and technique. Awareness of our movement doesn’t stop being useful or necessary when the class hour is done. Changing your movement patterns, whether removing bad habits or inculcating new ones, is a long-term process. Whenever you’re correcting something to preempt, or fix, an injury or to optimize your technique for maximum force, lasting change requires consistent attention to staying in and returning to good position throughout the movement(s).
The problem is that we have both our environment, which isn't designed for optimal human movement, and layers of habitual movement patterns resulting from living in that environment (plus other factors, of course). An hour spent moving with great posture and technique is incredibly useful, but for those changes to stick that posture needs to translate into your daily posture, into your daily movement.
...make your everyday stance your combat stance. — Miyamoto Musashi
But how can one do that? By gradually learning to sense what good position feels like in the body, without needing to either check a mirror, video, or have a coach point it out. Learning how to use your felt-sense to detect, and correct, old habits you're working to clear is a constant journey.
A few personal examples: a few years back I became aware that when standing my feet would be rotated out, I spent the next couple days switching my feet between the old pattern, rotated out, and the pattern I wanted, feet pointing straight ahead. With a feel for what being in each position was like I was then able to do quick check-ins throughout the day to see if I was in good position. After a few months those check-ins became automatic. The old pattern still hasn't completely been removed, but it's losing its hold. An older one that is gone, outside of certain contexts, is favoring my right hip while standing. My current project is learning how to keep the neck relaxed.
Why spend all this time on improving your position in the first place? Practically: to prevent injury and to move more efficiently. If you've trained your body to know what good positions are, then even when you're tired or fall out of awareness of your movement the body will continue to move well, without compromising your structure for the sake of some short-term goal.
From a holistic perspective these gradual improvements in your daily movement patterns will make for a more joyful experience of moving your body.