There are plenty situations your next move is independent of the move of your opponent.
I hereby suggest a feature to automatically make your next move after your opponents move. As soon as you played your turn, the play buttons are replaced by autoplay buttons. If you click it, for a card, that card will automatically be played after your opponents turn. (clicking it again will undo it, clicking another card's button, will make that card the next played card instead.
With this I particularly have slow games in mind, which can be played faster this way. (If you don't have swift cards to play, of course.)