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What I have personally found over the course of several seasons now is that I cannot push on the big toe and maintain ankle flexion, and in fact am now finding that actively dorsiflexing especially at initiation helps clean up turn entry and keeps that ankle closed without leaning on the tongue of the boot. It also shortens that leg slightly. But it takes a very concentrated effort as it's not an engrained habit yet.
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I think what you are concerned about is why some instructors tell skiers to put their weight on the ball-of-foot in order to keep the front end of the ski weighted, or to press down with the big toe. And now you are being told to lift the toes/front of the foot. You are worried that the shovel won't get enough weight on it. There is a clear contradiction here. Battles have been fought over this issue.
Worry not about that shovel. Contracting your tibialis anterior to tilt your lower leg forward, so that the shin rests on the tongue of the boot (tongue-shin contact), is step one in putting enough weight on the front of the ski to get it engaged. The big toe and the ball-of-foot don't need to press down. What replaces that is the shin pressing down, and when it presses into the tongue, the shovel is pressed down against the snow.
So there's more to getting shovel pressure. Step two is getting your body weight forward enough so that it hovers over the shin and boot tongue. This hovering presses down on the shin/tongue, and that provides leverage against the front of the ski. The boot works as a lever, pushing the front of the ski downward onto the snow.
To get your weight forward enough for this to happen, you need to position your hips and torso up and forward properly and be sure not to sit back.
Once you have shin-tongue contact and the hips/torso in the right place to lever the tongue, your shovel will engage just fine without any active ball-of-foot or big toe pressure.
The advantage of doing your stance this way is that you can now weight the back of the ski. Keep your heel fully down in contact with the boot sole. Target your body weight onto the back of the arch-front of the heel area of your foot. That spot is right beneath the tibia, where all your body weight comes down onto the foot. targeting your body weight here weights the tail of the ski, so it doesn't wash out. Not letting that tail wash out is a big deal.
So with tongue-shin contact, you can weight both the front and the back of the ski, and get the whole board to grip the snow, bend because of turn forces, and take you in a circular path around the corner. It feels great!
When skiers move their body weight onto the ball-of-foot, this lightens the tail of the ski and encourages the tail to pivot around the front of the ski. Getting the whole ski to engage, bend, and cause your circular travel is difficult if the tail is washing out because it doesn't have any weight on it.
Does this help?