Ouch. You are right. I really wasn't thinking about what I was saying when I used the words"two foot jump". That wasn't a nit pick, that was a major mis-statement.
I assume most skaters do push off with both feet (at least that's what I, an eternal novice, was taught) - but not at the same time.
And that statement also took attention away from the point I was trying to make, that "edge jumps" use the toe pick too.
The jerk that all figure skaters get on landing (including in the video) because they land on the toe still looks ungraceful to me. It would look smoother if they landed without the toe pick, even if they lost a little distance.
I had a problem trying to do toe loops. Only my drag pick (the one farthest back) was still sharp. (When I trimmed the toe pick, because I am running out of steel on my blades, I didn't pay any attention to creating sharp corners on the other teeth.) When I planted the toe-foot on the ice as far back as my coach wanted, all the picks came into play (in sequence), so I skidded on the toe pick while taking off. It hadn't occurred to me that anything but the drag pick mattered, but reaching far back changes everything.
The thing is, I get the original poster's attitude. Except for the brief times when you are using them, toe picks are a major nuisance. And if we have to have them, why is it considered bad to push with them? It's just one more way that figure skating is hard for people with limited flexibility.
Yes, Of Course "Edge Jumps" do still use the toe pick, but the main reason why they are different than toe jumps is not because they are one or two foot take offs, but rather where/how you generate angular momentum. As you yourself have experienced, the toe pick allows you to get more contact on the ice, which is why generally skaters generate more high on toe jumps than edge jumps.
I am not certain what you are referring to as the "Jerk" but the use of a toe pick on a landing is a matter of biomechanics. If you land flat footed you are causing your body to absorb instantenously a force equal to 9 times your body, which is an impact that is absorbed by your knees and hips alone. If you land toe-heel, you are allowing your body to absorb the impact force at a slower rate (although we are talking microseconds) through several of your lower body joints primarly your toes, ankles, knees and hips. This is the reason why if you land toe-heel it is considered softer, since you generate less sounds because of the progression of the impact. This is the same thing that occurs in Ballet and why Ballerinas are trained to land toe-heel.
Also, Dear God please do not sharpen/grind your drag(or anyother ) toe pick... If your blades are running out of steel, you need new blades. If you are grinding away at your drag toe pick, you are destroying the toe pick, which will make spins, turns and any edge jump virtually imposisble. Brut force might save your toe assisted jumps.
Furthermore, if your toe picks are a major nuisance for you then your blade is too advanced for you. You need to know how to properly use and control your blade before advancing to top level blades. A huge toe rack for beginners, can cause major technique problems specially on toe assisted jumps since it allows you to pick more randomly and still get away with it when doing singles.
Please, don't feel offended by my replies, I am simply trying to explain why a toe pick is actually necessary and soundly based on both physics and biomechanics.