The machine just asks for a tip and lets you put a % or $ amount in, usually with a suggested amount. I'm not sure what difference you perceive here between writing it on a piece of paper and entering it on a terminal.
Then the waiter returns with the machine, enters the total (including tip) - you touch your card to the machine (and if the amount is high enough enter a pin.)
The waiter does not handle the card.
There is no awkwardness at all.
I recently joined a newly-arrived US friend at a restaurant, and he paid, but clearly didn't understand the edit-the-bill process, so we tipped in cash then gave quick education.
It's a system that works well, is effecient and secure. Overall you stay in control of your card and your card is only processed once.