I think some of this is dependent on the hardware used? At least for Apple/Google Pay, I've noticed that for some merchants (Safeway), I can "pay" at any point while the cashier is still scanning times, while for others (Trader Joe's), I have to wait until the cashier is done and moves the transaction into the payment phase.

On the other hand, I don't recall a merchant where I could physically insert my card whenever I wanted, so the A/G Pay option is better in many/most places, even if there are some where you have to wait.