For a quicker shot, I shoot right off the tripod, but I toss a lightweight shooting bag over it so I don't have hard to hard contact. I shoot the local PRS matches to improve my skills, and I use the shooting bag over all sorts of stuff.
I taught two new hunters how to shoot off the top of a tripod in the kneeling position. Dad carried the tripod, pointed one leg towards the deer and set the bag on top of it. The kids were taught to point the rifle the way the front leg was pointing, and how to find the deer over the top of the scope and then move to the sight picture. They were very fast to acquire the target and made perfect shots. I had them practice with my .22 rifle, and it made a huge difference.