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.
I've seen systems where you input the final sum you want to pay, and systems where you can input the tip separately.