Hi Torsten
You are correct I use the board for the training and starting at the beginning. For me, I try and treat the training like a proper game, over the board (which it is

) and it tends to cut out my habit of playing any move because it's not a real game! So you do concentrate more. With full random training you do feel as though it's a proper game.
The board has to be in sync with the screen and you will quickly get used to the subtle dink or beep when it is not in sync. So for example you will get a beep if you make the wrong opponent's move and you have the advantage that the computer will announce your opponent's move. You hear a little dink when you bring it back into sync. This is helpful with Internet games as you will inadvertently play the wrong opponent's move, so you quickly get a warning. You concentrate on the board not the computer screen.
It is possible to use the board for input, but in practice you would probably not do so. This is because in order to back track to the start of the new variation you have to get the board in sync with the CPT screen and therefore not worthwhile. It obviously does not work for the recall positions. That said I have used it to set up King and pawn ending training.
I will use the 2D screen for lots of training because, yes, only using the board would seriously slow you down. The board is an extra option which for me improves the quality of the training (and indeed the internet games) when I want it. As with all things what is right for one is not right for another. See, if I took more care when facing a 2D screen I would have less need for the board - but alas I do not

.
Best regards
Dave