Where are you buying that you have to enter the amount into the POS to open the drawer but not to start the card transaction?
You can't consider the time it takes to enter the amount only in the case that suits you. If you have to enter the amount for cash, you have to enter it for the card as well.
You have to enter the amount the person is actually delivering... If the total is 18.45€, I'll probably be paying with a 20€, which the cashier has to input.
Now that I think of it, I guess not all POSs require that (the cashier does the calculation for the change in their head), but in my experience they aren't common.
Oh, what people do over here is "count up" to the amount. So if you give them 20€ for 18.45€, they go "5 cents to 18.50, 50 to 19, 1 euro and that's 20, here you go". That's a pretty fast method.
You can't consider the time it takes to enter the amount only in the case that suits you. If you have to enter the amount for cash, you have to enter it for the card as well.