Performing grabs and tweaking them definitely scores higher with judges for style. While grabbing and tucking stabilizes spins, flips and corks (off axis flips) in the air by reducing your mass moment of inertia about your center of gravity, it also is difficult in that it takes control and awareness because you have a approximately 10 pound object strapped to your feet which also limits your limbs ability to move independently. This is the main difference from trampolining and snowboarding in terms of mechanics. If you can find a cheap snowboard (the cheaper, the better perhaps because cheaper equipment isn't usually as light) and you can tape up the edges to protect your tramp surface, try jumping on a trampoline to get a feel for the difference.
Therefore, the ability to strike "poses" with different grabs and exaggerate them for effect demonstrates control which is why it given technical credence. It also looks pretty damned cool
Here is a video on the "method" air (a backside shifty combined with a tweak melon or lien grab), the most infamous grab amongst boardsports:
As to your general interest in designing and building a cross-discipline trampolining program for snowboarding, I would personally find myself interested in it as a way to progress freestyle. However, from a braoder snowboarding prospective, I would estimate there would limited interest in a purely trampolining program. This is because of the approach and philosophy snowboarders have for freestyle. Most snowboarders learn and progress through use of the ATML method: approach, takeoff, maneuver and landing. The approach and takeoff aspects are something that can't be taught by trampolining and this is where foam pits, air bags and progression parks (features that get gradually bigger) are of the biggest value. The approach and takeoff aspects are also the most critical to building a foundation for freestyle and dialing in new tricks as well as progression.
So, while trampolining is a valuable tool in learning (mostly the M=maneuver aspect) freestyle, it's really only so when included as part of a more complete snowboard training program. A very motivated and educated student might be able to piece together his own program and make use of a trampolining only program, but they are going to be a smaller market.
Hope this helps, good luck.