It does to be done safely. That's why in some cases it is considered technical diving as opposed to recreational. Think about diving in a cave with people walking above you that you can see. They can see you. And know that if you do come off the tether or have some other kind of serious problem you can be staring right into each others eyes as you die if you are not able to get back to the hole. No way you are going to claw or dig your way through the ice. And no way for them to get to you in time. They can't just bust through with hammers. They'll fall in and drown or go into hypothermia. They have to somehow get you back to the hole before you run out of air. Or you have to to get yourself back there.
Although if you have really strong people on the tether and the ice is not broken up and full of ridges, you can get inverted with your fins on the ice. Add some air to the suit or bc and have them pull really hard. Waterksiing, upside down, under the ice. But it's best to plan it that way. Giving pulls for an emergency just to get a good pull so you can ski is a good way to piss tenders off.
Although if you have really strong people on the tether and the ice is not broken up and full of ridges, you can get inverted with your fins on the ice. Add some air to the suit or bc and have them pull really hard. Waterksiing, upside down, under the ice. But it's best to plan it that way. Giving pulls for an emergency just to get a good pull so you can ski is a good way to piss tenders off.