Balancing over the ski in transition is the deal... All too often though, for many unless properly coached, shortening the inside leg without containing the inside foot gets people inside and back. If I can sort out the 'over' in that moment before transition and sort the feet out, then we're ready for long leg, short leg and maybe even leveling the pelvis.
I don't follow the balance on the inside edge versus the entire ski distinction, but
@markojp nailed it.
The balance
around transition, when the skier is not standing strong on a grinding ski is the deal. When the ski is grinding, bending, you got your pressure, it's turning whatever, that's the easy part. With enough training, wine abstinence
and tuned equipment, anyone can stand on one foot
Developing balance on an edge that's not really "there", as your body parts are re-arranging for the new turn, that's the magic trick and it's all about the dynamics, not the statics of COM/BOS balance as you're grinding.
The point being - as you're moving up the stack, you have to stop grinding the ski. So although normally presented as expert level, balancing on a grinding ski, at whatever angle you can think of (including hip to snow), is just the entry level for true performance skiing...
That's why imho, the true measure of an expert skier is not doing whatever GS carved turns on a SL ski on a black run, that we see everyone doing all over youtube (where all you need is big angles and grinding the ski) but doing true slalom turns on a black run. Grind that!