Interesting question…
Balancing postures require three parts; physiological, respiratory, and emotional or mental. If one only works the first, then it is up to the teacher you have chosen to direct you into the others. Additionally, since there are three parts, if you are only working the first you can expect 1/3 of a result. This is not exact, of course, but you get my drift.
With regard to your outer edge comment…
In my practice and teaching the foundation of standing poses mandate a rooting in the toe mounds and inner/outer heels with a subsequent lift in the arches. This rarely changes in standing poses though I would imagine in whatever toe balance is this would be impossible.
If your left leg is not as strong please remain on that side of the pose for 6 more breaths so that you do not etch your current imbalance any deeper, again something that should be coming from your teacher.
The awareness must be placed in that which is used (so it is used) and that which is not (so it is not). In other words there is a dualistic nature in the posture and that must be maintained. Some muscles need to be used powerfully (without aggression) while others need to be kept soft and supple. Additionally if action and alignment have been forsaken it is far more difficult to have a fruitful flow of energy in the physical body.
Generally speaking, when students struggle with balance there are modifications (in the practice I teach) to assist them as they develop. This empowers the student to work on other elements without adding balance to the mix but the student must eventually grow away from the modification otherwise it becomes a crutch.
There is so much yoga to be worked in yoga. I don’t disagree with “practice” I just happen to believe that phrase transcends the anamayakosha.