When you're doing Levitation exercises on the Ladder you're strengthening your posterior chain: primarily your back muscles and your glutes. And it's called "levitation" because you're floating up against gravity. Then wouldn't using a strap be a little bit of a cheat?
This video makes the exercise look deceptively easy. There's alot going on. One of the most important aspects of core strength is stability. In this exercise you've got to stabilize in all three planes of motion.
The Waterfall series on the Ladder or the Archway is the absolute best for pure front of the body core strengthening. While you're working the same muscles as a sit-up or crunch, you're asking your body to do the same thing in the opposite direction. The extra space you gain by being off the ground allows you to add fun variety, like Press Ups.
I recently recorded several exercises in the Levitation series and as I was selecting which exercises to use, I looked back at old syllabi to see if I was forgetting any really cool ones. I was. I haven't done Snake in years and I remembered how much I've always liked this.