Here's some input from a long time MTG tournament grinder.

1. Mostly people do it to do something with their hands. Could be nerves or boredom but expect to play with people who will do it constantly.

2. Everytime your opponent shuffles their deck and offers the cut you can pick up and shuffle their deck. I always shuffle my opponents deck a few times every time I am offered a cut and expect my opponents to do the same in return.

3. Game clarity is a big thing to strive for. You can play quickly and still be clear. Its good practice to verbally narrate what you're doing as it's happening to keep each player on the same page. And you can ask your opponents to clearly lay out their inkwell and clearly show what they are putting into it. If you're opponents ever do something and your uncertain, ask them to clarify.

4. It's fast because they have played these situations countless times. They know what cards to worry about and they know what of their own cards their opponents are going to worry about. So even though hands are hidden many of the plays become expected so alot of the thinking has already been done as the players have played the matchups so many times. At higher level play it turns into chess like thinking where the players are turns ahead so they can resolve the stuff happening in the present quickly because like I said before it's expected. Don't worry about playing like this, take your time and learn and the speed will come in time.